What methods to you use to determine what kind of hardware you need for a server?
I often find its very hard to predict what kind of hardware you will need for a web based application with a database.
Do you have any good methods or recommendations on how to best pick hardware to use?
It really depends on your web application demands and traffic expectations.
Very few websites will need more than one reasonable dedicated server within the first months. And if you do, then you can probably afford to buy more hardware ;)
I guess that your web app is not a critical business application as you said "a server" and "a database" otherwise you should perhaps look for some means of redundancy ?
At work we have some guidelines about the hardware, and the latest suggestion is that the server should be 64 bits as SharePoint 14 looks like a 64 bits only version.
If you can afford it I would recommend that the SQL server should be 64 bits as most people agree that adding more RAM (above 4 Gb) really pays off.
To add to what Charlie says, once you have a workload model you can feed this into a simulation of your system to determine the horsepower you need to satisfy that load. There are some tools that can do this sort of simulation:
This stuff isn't easy, and the commercial tools will cost ya.
You could also try looking for a benchmark that's close to your expected load and see what systems give you the performance you're looking for. The TPC benchmarks would be a good place to start.