I am a longtime amiga 500 owner (going on 17 years). I am still using the original Amiga 500 I bought in 1986. It is true that this system does not come stock with a hard drive. However there are lots of SCSI controllers for this machine such as the A 590. CD-ROMs and hard drives are easy to get, and are also dirt cheap. A lot of classic original games for the Amiga, came in Non DOS format, which prevented copying to either other disks or hard drives. There's software available to install a lot of the non DOS games such as WHD-load.
It is true that the Amiga 1200 is a fantastic system that runs AGA games. However, there's tons of software out there, that was written specifically for the Amiga 500. If you wish to take a chance to purchase a real Amiga system, I would have to argue strongly in favor of the Amiga 500. The main reason simply price. They are a dime a dozen on ebay right now. In fact I have 7 of them. If you wind up being disappointed, then the investment is minimal. They are tough as nails too, as the beer stains, and cigarette ashes inside mine can attest to.
If you like the system, you can either expand the A500, or invest in an A3000/A4000's. I have always been in awe of the bigger Amigas, but have never actually purchased one as I have always been content with mine by expanding. Now I can burn music or data CD's, play music, or with a simple double click, revert the system to play the very first Amiga Classic game I ever purchased, (Darkside). My first PC is long dead, and is now stripped and reborn housing a SCSI CD-Writer, SCSI CD-ROM, and 6 GB of Hard-Drives externally connected to my A500.
There are a couple of issues to consider. First is the monitor (Commodores A1084/1084s). You need this to run the games. A520 Modulators that allow hook up to a normal TV, are not well suited for games( the original intent for the system). Next is the floppy disks. They are 720 KB, getting old, and harder to find. They are not the same format as PC 1.44MB. They are not readable with PC's either.
The monitor, and 1 hard-drive are the hardware failures I have experienced, that were easily replaced at inexpensive cost. As time marches on this will no doubt change...
I strongly suggest you first try Cloanto's Amiga Forever. I run it on Windows XP and find it quite amazing. I can assure you of one simple fact despite my argument in favor of the A500. You will enjoy ANY Amiga you decide to obtain!!!!