Firstly, join the unofficial mailing list. There's a whole heap of helpful people there.
The most powerful cards supported are the Voodoo3/4/5 cards.
With OS3.9 you can switch it to use 'other memory' so you preserve chip ram. My setup uses hardly any chip ram at all.
Not sure about DPaint, but Brilliance needs chip ram and don't work well (if at all) on promoted screens.
I don't recall anyone ever mentioning any sucess with built in TV out, however, many TV cards have support. By linking the Amiga's monitor output to the TV cards composite input, you can run 'difficult' programs like Brilliance and Scala in a window. HDD installable games work well this way.
Being able to use an Amiga with high resolution screens is so much better. I dare anyone to _want_ to go back to Hi-Res interlaced after using WB on say 1024x768x32@75Hz, it's a nightmare.
I've not seem any overheating problems. I've got my Voodoo3 overclocked to 182Mhz from the 166 standard and I've not had any problems at all.
Regards
-john