@retronerd
Welcome to A.org :-D
As others have said, there are currently two main routes you could take, however you could also get yourself a A4000 with a PPC card - that'll run OS4 when it's released, as well as OS3.9 for compatibility with older applications that need the AGA chipset. That said, the old "Classic Amigas" are old, starting to fall apart, and PPC accelerators are very expensive.
The new Amigas are the "AmigaOne" series, based around the "G4" and "G3" PowerPC processors. First released a couple of years ago were ATX models (primarily the "AmigaOne XE"). This is a great system for expandibility, but if you get one second-hand, ensure that it's been fixed (they were originally shipped with a couple of hardware bugs). The latest model is the "MicroA1", which is cheaper and fits a Mini ITX case. It's less expandable however. Both these boards run AmigaOS4 - a PowerPC native version of the AmigaOS, but with many nice features (Eg limited memory protection, looks nicer, built-in TCP/IP stack). OS4 will also eventually run on PPC accelerators for the "Classic" Amiga. Currently its out in pre-release form for the A1. AmigaOne types tend to hang out around
AmigaWorld.
The Pegasos, as already mentioned, is an Amiga clone, also using the PowerPC processor. It runs an AmigaOS clone called "MorphOS" which is currently in a further state of development than AmigaOS (although there have been some serious problems with development recently that I won't go into now). MorphOS is designed around a different philosophy to OS4: MOS will probably be slightly more compatible (bear in mind that neither will run chipset-bashing programs other than via an emulator), and they plan to implement a completely new set of APIs at some point. The idea behind OS4 is to slowly bring the AmigaOS APIs up to what's needed nowadays - for instance, once enough software is written in a system-friendly fashion, full memory protection will eventually be turned on at some point. MorphOS users tend to hang out around
MorphZone.
There's also AROS, an open-source Amiga clone. It's the least developed of the three, but will run on your PC at least.
---edit---
There's a review of the A1 and OS4 on a mainstream tech site
here