Your support software should cater to your needs, depending on how your business operates.

Fiver uses Vanilla forum and Zendesk.
Thumbtack uses Zendesk.
Not sure about AirBNB, their help center seems to be custom.

Depending on how well funded your are, I would recommend starting with a free plan with one of the help desk SaaS products, or even using open source ticketing platform. Then, as your needs grow and you need integration with your marketplace, there's no reason you can't scale and migrate.

This really depends on your target audience but Zendesk allows for scalability that most startups need. You would need to gauge the level of knowledge needed for your agents - which is dependent on your startup industry.

For example, if you are a company like AirBNB, you may not need an extensive knowledgebase for your outsourced agents because the website users are not going to ask specific programming questions. However, if you are a technology company, your agents may need backend white-papers to help customers solve functionality problems themselves.

I always recommend to use a third party, and I would recommend Intercom (http://www.intercom.io/). It has instant support service to have a conversation with the users. You can always use it to create automatic messages and emails to your users, even use segmentation for those messages.

I know Airbnb uses Mixpanel, but for metric purposes, to analyze their users and their actions, but that's not exactly support: https://mixpanel.com/case-study/airbnb/

Zendesk is one of the preferred systems being used by many marketplace startups and other global brands including, say Slack. It is extensive and scalable as I have used it at advanced level.

The advantage with Zendesk is that you get an excellent support center too, for knowledgebase articles. See an example of KB that I have developed for KarmaCRM, at: http://support.karmacrm.com/hc/en-us/. See few more at: http://in23hours.com/

GrooveHQ is another good option, https://www.groovehq.com/

So we work with many startups and large organizations; from my personal experience it looks like more and more startups particularly are seeking outsourced custom software solutions for their teams. Many startups are now conceived by non-technical founders who need CTOs to develop the prototype, this is where companies like Betabulls.com has been really capturing the market for custom software because of the unique problems some of these startups face - not typically off-the-shelve problems. Airbnb for example did custom web app once they pivoted but they did that themselves otherwise they would have probably hired just like many others do.

Looks like this question was 3 years old. Freshdesk has come a long way in past 3 years. I will recommend trying Freshdesk, with their new market place it opens up possibilities. If you need any help with Freshdesk, send me a note or call me.

I will not suggest a custom support software, but I will go with Zendesk.
Zendesk is a suite of support apps that helps transform your customer service into agents for customer retention and lead source. It has one of the most flexible plan structures, making it ideal for business of any size. It consists of support, chat, call centre solution and knowledge base modules that you can upgrade separately. However, its support plans include the basic versions of chat, call centre and knowledge base, so you get all sides covered right off the bat. This setup affords a start-up or small business to implement at once an industry-class help desk. They can easily upgrade to more advanced tools like CSAT surveys, web SDK, IVR phone trees and answer bot as their business requirements get complex. Zendesk Support puts all customer interactions in one dynamic interface for an efficient, seamless process. You can bring in customer queries from almost any channel via pre-defined ticket responses, web widgets and customer search history, allowing you to respond faster and with the right context. The main module can also be customized to fit your customer service workflows or apps that you are already using. It also features customer satisfaction ratings and analytics via performance reports and dashboards. The software also lets you develop institutional knowledge culled by your customer service over the years. The Guide module helps you build a help centre, online community and customer portal. You can direct FAQs and low-touch tickets to this portal, while your agents deal with high-value customers and leads. An AI Answered Bot can also direct queries to relevant articles in your base, squeezing out more ROI off your content marketing budget. Zendesk also gives you the option to set up a call centre with web, mobile and messaging channels. This is ideal for highly engaged customers or prospects; your agents can instantly connect to them via automated trigger. Through the integrated live chat, your agents can also proactively engage customers on your website or ecommerce page. You can also use analytics here to make sense of the conversations collected by your call centre. As for the Zendesk Live Chat, it is one of the simplest but best ways to engage high value leads when they land on your website. Studies have shown that customers are three times more likely to buy when they get chat support right when they need it. The chat comes free but can be scaled for unlimited chats, conversation tracking, widget unbranding and other advanced IM tools. Its latest app to date, Zendesk Message levels up your chat support by engaging customers in their favourite messaging apps. Instead of waiting on your website for prospects to ask questions, this tool allows you to follow them wherever in social media they are mentioning you. The message tool integrates with Facebook and Twitter and is available through the Chat module. Overall, Zendesk is a comprehensive and focused help desk suite with all the essentials your support needs that you can scale according to your growth pace: ticketing system, knowledge base, community forums, live chat and call centre. An IT Help Desk edition is also available.
Zendesk Benefits are as follows:
1. More than just ticketing: Zendesk is more than just a help desk. It crosses over to CRM because it allows you to organize processes, workflows and tracking of customer engagement. On its own the software can turn your huge volumes of support data into a treasure trove of leads, opportunities and market insights. Zendesk helps you consolidate these data and leverage them to build or nurture long-term relationships with your customers. To fully leverage CRM, Zendesk integrates with popular solutions such as HubSpot and Zoho CRM. This means the data you collect in Zendesk can be consolidated for further use to develop marketing campaigns and funnel potential new leads into your sales pipeline.
2. Scale your customer service: Zendesk is a comprehensive suite of support apps that you can scale as your business needs grow. You can treat is as an end-to-end solution, structuring around it a help desk, live chat, knowledge base, call centre and community portal. Or you can start with the main support module and build your support architecture along your budget line. The main support module comes with the Lite version of chat, call centre and knowledge base. You can say you are getting these add-ons for free, so your help desk does not start bare, rather, it rolls out built with industry-class tools. The whole pricing setup of Zendesk lends to your support reliability and scalability, and to your cash flow flexibility.
3. Engage high-value prospects: Proactive live chat with automated trigger lets you engage prospects who are lingering on your website or checkout page and help. You have a small window to convert these prospects while they are interested in your product, and the live chat connects you to them in real time. Moreover, studies have shown that customers are three times more likely to purchase when given chat support in real time — right when they need assistance. Prospects who linger on your product page or checkout page may be confused or having second thoughts; the live chat links you up to these near-to-convert leads at the right moment and lets your support agents, or maybe sales, do the finishing touch.
4. Go where prospects are: The Zendesk live chat on your website is great at answering queries in real time. But it sits there waiting for prospects to come to you. To complement this setup, the vendor rolls out a messaging tool that allows you to reach out to customers and prospects in their favourite messaging apps. It lets you follow leads where in social media they are talking about you. Messaging apps are becoming the primary driver for customer service, too, and this tool ensures you got this area covered. Where a complaint or negative comment is lodged on a social media site you can quickly address it before it escalates.
5. Maximize your content: Zendesk features an AI-powered bot that you can use in the Guide module. The bot surfaces relevant content in your base as customers type their query. If you have an archive of practical guides and articles sitting unused in your website, they can now add value to your customer service via this bot. That means you are getting more ROI from your content budget.
6. Self-service: Zendesk allows you to build a self-service customer portal using its knowledge base and community features. Combined with the AI-powered bot that can direct FAQs and low-touch tickets to the portal, the self-service feature takes repetitive work off your agent’s shoulders, so they can focus on high-value tickets and promising leads. It levels up efficiency in your customer service workflow.
7. The Essentials of a robust helpdesk: The software has all the key features you need in a powerful help desk solution. It has got ticketing system, knowledge base, community forums, call centre, live chat and messaging tool. You can build an efficient and powerful customer service process around this structure, if not at once, one module at a time. For IT assets, Zendesk offers an ITIL-ready IT Help Desk edition. Likewise, it integrates with important business solutions like CRM, salesforce automation and over 600 apps in its marketplace.
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath

Honestly, UserVoice and Zendesk seem a little expensive

Fortunately, you can find alternatives like Kayako, which allow you to run your customer support department for only $15/month per agent, which is a bargain for everything you get:

Live chat + email + social media - unified channels support
Self-service center
Mobile SDK (Android + iOS)
Insightful reports
Team collaboration features
Assignment rules
Collision prevention
700+ app integrations thanks to Zapier.
You also get a Customer’s Journey, which allows you to visualize everything your customers have done and said, so you can bring context instantly and solve their issues ASAP.
Conclusion- There's no platform deemed to be 'Best' choose what suits you.

I hope that helps!