If you are just interested in trying out the Amiga to play some games, I would suggest an emulator like Amiga forever or pick up an A500. Even a nice 2000 will do the job if you don't mind the big box. Plus they are bomb proof but the downside is they use SCSI drives which are scarce unless you consider the SCSI2SD card option. As for Amiga games. I loved Pirates!/Civilization/Railroad Tycoon and The AD&D adventures such as Pool of Radiance series and Eye of the Beholder were good fun.
If you decide on an AGA machine (1200/4000) then you can end up parting with a lot of cash, especially if you go to Ebay. Prices can get crazy especially once you factor in Accelerators etc.