Great idea! If you've got the cash, inclination, like to tinker and are patient - can't think of a better hobby-computing experience than an A1200 (or any Miggy really). Advantage of the 1200 is the readily available processor upgrades (and yes, an 060 is THAT much better all around for an ultimate Amiga experience), but for games only and some other minor utility type stuff - a high end 030 (50mhz) might be plenty. I'll admit, I had more fun upgrading and enjoy my big box Amiga than I ever did my A1200, but either way - you'll be happy tinkering with a 1200 if you're just used to a 500.
BTW: plan on spending a small fortune no matter what you do Amiga wise and Jens' Indivison AGA (native VGA out) is also highly recommended. OS3.9 on an 030 equipped A1200 *is* going to seem a little sluggish today - FYI, but it is what it is. Tons of patches to get the most out of your system on Aminet and here. If I were to go back to a 1200, the Boing Bag 3 patches would be a must for me, now that I'm used to an 060 machine.
Enjoy!