My general rule is CRT for anything PS2 and older. Xbox and GC generally look OK on more modern displays, but PS2 looks rougher. Plus, there aren't many lightgun games on Xbox and none on Gamecube. Some people rave about RGB or component on a CRT, and that looks great, but I would take PS2 vis composite on a CRT over using component on a flat panel. So if you can't get a crt with component, RGB, or SVideo, don't worry too much about it. It's still better than the alternative of playing it on a flat screen.
As for your other questions, I believe PS3 will output 240p via it's analog output just like a PS2 will. Framerates aren't enhanced by BC PS3s, and some of the later model ones (after they removed some of the BC hardware) actually had performance issues with some games. Also... Don't spend a bunch of money on a BC PS3. They brake all the time. If you find one cheap or one that has a warranty that's 1 year plus, then maybe. But in my experience they aren't worth the effort. If you do buy one, make sure you can test it. Make it play a PS3 game, not just a PS2 one (but test that too). And make sure it connects to the internet and try to do a system update, unless you intend on running old firmware forever. They do a system check when they try to update, so they will sometimes fail the update but can't revert to the previous working state. So they get stuck in an update loop that can only be fixed by solving the hardware problem. This includes issues with the bluray drive. That's why I said to test PS2 and PS3 games, because I've seen them before where they read PS2 games, but no PS3 or Bluray discs, and then they won't update and you have to replace the laser, or re-seat the ribbon cable that connects the drive to the motherboard. And that connector is fragile and breaks all the time. And that can cause the drive check to fail and cause an update loop. This doesn't even include issues like the YLOD.
