About Selenium (and only Selenium as I don't know WatiN) - it can only do what you can do in your broswer. It can click, type in fields, submit forms, take screenshots (that's a very good one), set up cookies (so yes to this one). You can always set up GET data through the URL. But I am not aware of any technique in Selenium that would allow you to set up POST data in any other way than navigating in a browser. Also, because the tests are in your browser, they are not particularly fast. E.g, on our product, a single thorough test with ~250 steps takes about 10 minutes on my computer to complete. Of course, you can always divide that between many computers using Selenium Grid. It's just more work.
To conclude it - I'd say yes, Selenium is good for your needs as there are so many ways to write a good test in it that everyone finds his style. It is good for quick checks, functionality affirmations, but also for full-scale tests etc. But if you want to do some really advanced stuff, then that's a job for a long time. Selenium offers so much functionality in so many different ways that it is definitely a full-time job to understand them and know how to use them.
Try Selenium-IDE for 20 minutes. It is just an addon for Firefox that can record your actions and then replay them. If you like what you see, go for it. If no, hire someone who will.
