It's useful to have all three programs installed if you have them. Personal Paint of course being free is the most practical choice, and I peronally use it the most anyway. It has a much larger undo buffer than Deluxe Paint, which only lets you undo a single step. Brilliance is excellent, especially for its colour depth control which is useful for working on OCS palettes on an AGA machine without having to reboot into ECS mode, or for working on Mega Drive/PC Engine/Master System graphics or for other limited-colour systems.
Still, I find myself using Personal Paint every day. I pixel icons, GUI images and game graphics. It has really good palette control and a useful Halfbright brush mode. It does just about everything I need it to, I usually only switch to Deluxe Paint for the onion-skinning and animation controls, or Brilliance for the colour depth stuff or painting in 24bit.