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For a decent frame-rate in Quake you'll need an 80 MHz 68060, either Apollo or Blizzard. Are you intent on towering your A1200? If so, I believe higher frame rates are possible via a PCI graphics card with the Mediator. Your A1200 will obviously need towering if you go this route.
Alternatively, you could by a Blizzard PPC card and a Blizzard Vision graphics card (all in standard wedge case). Therefore you could run PPC versions of Quake (faster). You could also run the 68K version being as though those PPC cards have either a 68040 or 68060 CPU as well as the PPC CPU onboard too. The Blizzard Vision has to be plugged into a Blizzard PPC board though, and they're both terribly expensive.
Now, if you're serious about display quality, I'd go for a real CRT monitor with an Indivision Mk. I. The Mk. II Indivision supposedly has problems with smooth scrolling/tearing in games, but I can't comment on that, maybe someone else can share their experience. Mind you, some people have got the Mk. II's working just as well so I hear via certain config. settings in the Indivision config tool...again, can't comment. All I know is that a good quality CRT cannot be beaten when it comes to gaming. Also, I find a flat screen takes away some of that Amiga (or retro) feeling. It's not easy to explain, and I suppose it's down to personal preferences in the end.
As for programs, most programs will let you specify the screenmode that it will open, therefore you can run them in any resolution you like. Only old programs will be locked to 640 x 200 NTSC or PAL for example (well, by old I mean 1980's LOL) but 9/10 times you can promote these to your specified mode, at least that's my experience on my A1200.
