The cd compilations although cool suffer from the fact that it all comes off the cd. There is also a lot going on gaphically with the menu system that tends to slow down the screen, the CD also slows things down.
Also you need a pal tv to do all this effectivley since the games run bst on a pal system.
A moderately tricked out Amiga 1200 system is your best bet as others have mentioned.
These days a PC conncted to a 42" plasma running UAE is my system. NO hassles, no Tubro cards, indivisions, and I do it with a wireless keyboard.