Copics over Promarkers, definitely. They're more expensive up front, but Copics come in more colors and are refillable while promarkers are not. The Tim Holtz markers are really a completely different product. I have them and love them too, but they're watercolor markers so the coloring style is very different. You won't get the smooth blending like you do with alcohol ink.
Full disclosure, I'm a certified Copic instructor, so I'm biased. There's some copic info on my blog, but right now it's woefully lacking in tutorials (I'm working on changing that, but for now www.inklingsandyarns.com/category/copics/). You should also check out Marianne Walker's blog (http://ilikemarkers.blogspot.com). She's the product director for Copic in the US and her stuff is amazing.
Let me know if you have any other questions or need help getting started. I typically check in here daily even if I don't post, and I can also be found on Advice from Groomz.
Hmm...it's hard to suggest colors because it really depends on the images you use and the colors you like, you know? For example, if you like to color people, you'll need a lot of browns for hair and skin, but if you're more into flowers you'll want a lot of greens and a few pinks and purples probably.
I will say that my basic "rainbow," is R22/24/27, YR04/07/09, Y11/13/15, G21/24/28, B21/24/28, BV02/04/08, and V12/15/17. The E30s are the most versatile browns, IMO (good for hair, wood, etc) and E0000, 00, and 01 are my go-to for caucasian skin. Then I also have a bunch of random favorite colors. BG70s are a really pretty dark teal, Y30s are a nice sunflower color, and on and on, so it's really a matter of picking your favorites.
I generally recommend that people start with a particular project they want to work on, and buy the markers you need just for that stamp or picture or whatever. Then you can expand your collection from there. Also, don't buy the sets. They seem like a better deal, but you end up with markers from completely different blending groups, so you have to buy twice as many more just to go with what you have. You're better off spending slightly more per marker and only getting the colors you want/need.