Welcome to APUG! And welcome to film developing. You're going to love it, and there are lots of resources out there to help you get started. As for chemicals:
Developer: This is the most crucial, and one picks a developer to suit the film and the look one wants to achieve. That said, Kodak D-76 is a great all-purpose developer. It comes as a powder and you mix it to make a stock solution, then dilute the stock as needed. Kodak HC-110 is also great, and it comes as a syrup that you can either mix into a stock solution (as instructed on the label), or better yet, there are tables online that tell you how to just mix a small amount of the syrup directly into a working solution.
Stop bath: Any stop bath is good, and some use a color-changing indicator dye to signal when it's no longer effective. Popular brands include Kodak Indicator Stop and Ilford Ilfostop. I like the Ilford because it uses citric acid and so it has no odor.
Fixer: Again, it doesn't really matter, but I like Ilford Rapid Fixer.
Yes, you'll have to push your HP5 400 two stops in development. The developing time tables at http://www.digitaltruth.com should help you out. Good luck!