AngelList is your best bet. Since you're asking the question, chances are you don't have a way to get introduced to these investors. The simple truth (like it or not) is the chances very low that you'll get a deal done without an introduction from someone they trust. AngelList can help with that, so can going to networking events. And finally, If you're the introverted developer type, you can also get their attention by just building something really cool on your own, followed by some serious traction. Arguably the best strategy of them all.

Assuming when you say 'vest' you actually mean exercise. It's sounds like an investor doesn't believe you will execute without the extra incentive. I'm not a fan of tranches of any form, but sometimes you gotta do what you gotta do. Also, you didn't mention the strike price, so no way to know if this is a good deal or not. My advice is to ensure you have an experienced tech lawyer, and discuss it with them. They will have the experience to tell you what is normal and acceptable.

Short answer, when you know it will pay off. Long answer, PR gets the word out people to your site/app. If you haven't proven (on at least a small scale) that you can convert these people to users/customers, then you're wasting your money on a PR agency, and worse, you might be doing harm to your brand. My advice is to build your first sets of users by hand, one by one, listen to them and adapt your product until you sense they have become emotionally connected to it. Then amp up your marketing mix, PR being the first (in my opinion). An initial contract could be $5k per month, with the sole purpose to position the company to publications that achieve a specific goal (fund raising, user growth, brand credibility, etc). Contracts will ramp up to $15k-$25k per month after you've proven the value.