I\'ll have to echo the opinion a lot of people have already mentioned - there\'s no one best paint, but there are paints that work better for different techniques/artists. So whichever paint you pick, be prepared for a learning curve of a mini or three as you learn how best to use the paint with your techniques and habits.
Personally, I love the Reaper Master Series paints. I previously used a mix of Reaper Pro Paint, Adikolor and a handful of GW, but since I bought my first lot of the RMS, I\'ve hardly touched other paints. They are designed for people who like to use layers and glazes, and work admirably in those regards IMHO. Some of the colours don\'t have the greatest coverage for basecoats, but that\'s due to the properties of pigments and will be true of just about all paints. (I suspect the new Foundation paints don\'t include bright red or yellow because you can\'t get them to cover, where you can get a brick red or an ochre yellow to cover better.) The colour selection is a really nice mix of vibrant \'fantasy\' colours and natural and dulled colours, both of which have their uses for painting.
Being able to purchase the whole Reaper set in one go would set you up pretty well, as the set will include bottles of flow release, sealer, anti-shine agent (add a smidge to paints that are a little too satin for your tastes), black and white primers, silver, gold and coloured metallics, inks, and paints designed specifically for doing lining, although they are also handy for shading and can be used as regular paints.
Being a big paint junkie, I did also purchase the P3 paints. The comments previously mentioned reflect my experiences - nice coverage, slight shine and plasticky feel (though you\'ll get that with some of the Reaper paints, too). It\'s been very hard for me to get the right mix of water/gunk to paint for my style of painting. What I find works for me when I want to use the P3s is to use a Master Series paint as the highlight colour I mix in. I\'m still on my own personal learning curve with these paints.
Unfortunately I haven\'t used Vallejo Model Color, so I can\'t add a useful compare and contrast on that. I have used a few of the Game Color, and didn\'t like them - very slick and plasticky, one time the basecoat wouldn\'t even accept shading layers, the paint just beaded up. Plenty of folks do use them, though.