PostgreSQL hardware reguirements
PostgreSQL is open source and you can use on almost any Linux/UNIX-like machine, plus Windows and Mac OS X. See the buildfarm for a list of known-working configurations. Precompiled binary installers and/or packages are available for popular platforms. I had some problems compiling it on AIX, but it was because I used gcc instead of IBM's XLC.

The minimum RAM you will need is 32MB, and you'll need least 50KB of disk space. As with any other database everything depends of the queries you are going to do, how many users you will have, what your performance requirements are, etc.

If you can, try to divide your DB between different physical hard drives (eg WAL on one, main tables + indexes on another), tune postgresql.conf to fit your machine, etc.  

I recommend that you to read Greg Smith's book PostgreSQL High Performance.