You basically have 4 options:
AmigaOS 1.x/2.x/3.x on a real Amiga
1.x may be better for older games. But if you plan on installing to hard disk with WHDLoad then go for 3.x as you will need this for large hard disk support and also for WHDLoad to work properly.
AmigaOS 1.x/2.x/3.x on UAE
Same as above for compatibility, but some games will not work properly and as you said your disks will not work.
AROS
This can run as a Native AmigaOS-like OS on x86 PCs. But it will not run any of your Amiga games. You would still have to run UAE within AROS.
AmigaOS 4.0 on AmigaOne
As with AROS, this is an AmigaOS-like OS but it runs on proprietary hardware (the AmigaOne). It will run some PPC software for Classic Amiga (I think) and also some 68k classic software through built in emulation, but for you games yet again you will need UAE to emulate an A500/600/1200.
So for your purposes, I think an A1200 with a big hard disk and OS3.1 / 3.9 would be the best option. That way you can install your original disks to hard drive and run them from Workbench.
Hope that helps.
