If you aren't tech savvy, I would highly recommend shopify. It's designed with users like you in mind with a very simple back end that can run shipping, adding products and everything else you've mentioned. If you can run a wordpress site, you can run shopify.

After setting up my first store I was able to get the next one up in only a few hours. It's that easy. Also a great community for support as well as an impressive app developer community with new features coming out all the time.

I have many years experience into ecommerce and with various platforms. I currently run 1 Yahoo store, 4 Volusion stores, 1 1shoppingcart store and another one on an old old platform that I won't even mention because it's no longer supported or offered to the public. That said it's should be clear to you that Volusion is my personal favorite. Keep in mind It doesn't matter which platform you choose they all have a learning curve and their own limitations. You'll need to invest time into learning all the in's and out's of the system. I have looked into shopify in the early days and found it very limited but i'm sure it's a whole lot better now. Big Commerce I looked into as well and it looked interesting but figured was already stretched out enough on different platforms that I decided I'd go with Volusion again. The things I like about Volusion is they have great live support and their support database is also well documented and up to date. Once you get to understand the system which isn't very hard and they've made it much more user friendly throughout the years it get's easy to make updates and change things around. Their built in SEO friendly system is also easy to work with. That being said, each plattform have their limitations so you'll really need to write down the main features you can't live without and make sure the platform offers it. Here's one example: We do "buy 3 get 1 free" on many of our products, however this type of feature isn't possible on volusion, so we found a work around and came up with "Buy 4 for the price of 3". Same thing you'll say but not really, customer needs to enter 4 units in their cart in order to get the discount rather than 3 so on a marketing perspective "buy 3 get 1 free" is a better seller. This is one of the things we had to live with.

I too would recommend Shopify. Built my business on for more than 3 years. Service was great, as was flexibility.

I'll caveat that it depends on your level of sophistication.

You mentioned you already have a website. What are you using for your existing website?

If you're using WordPress already for your site you could use WooCommerce. It's a plugin for WordPress so it seamlessly integrates into your site. It's bigger than all of the other platforms out there (Shopify, Magento, BigCommerce, etc) and has a ton of integrations.

If you find WordPress confusing or you don't already have it setup then looking into Shopify would be next best course of action.

I hope that helps! :)