I definitively recommend Selenium, you can use it from .NET, supports different browsers, works in automatic builds and CI processes (we use it from CCNet). The code is stable. It has a few quirks, but after all they all do.
Whichever tool you choose, I recommend making your own test facade class(es) around it. The facade should be designed to suite your concrete testing needs, without exposing too much the details of the testing tool’s API. This will make the test code easier to write and maintain.
UPDATE: if you use ASP.NET view state in your app, you could have problems using a pure HTTP test tool. This is where browser-controllers (like Selenium) are much better.