Form my own experience.
I first started to learn how to paint with the Battle Games in Middle Earth series from Deagostini. It was a great way to learn how to paint. You got one painting workshop every two weeks (with either 12 plastic or 1 tin figure). I would sugest that was the nicesest way to learn how to paint. Step by step.
When you paint your first mini, be glad if you paint 'within in the lines' with all flat collors. If you get the hang of that than start by aplying washes to you mini's. After that try drybrushing. After that highlighting. How I used to paint my mini's was: undercoat (black), basic collor, wash, and first highlights and when needed second highlights. Most of the time that will give a pretty desent mini (by my standaards anyway).
What paints to start with depend on the troops you are going to paint. Always buy either black or white as udercoat layers. If you are using natural collors, 2 shades of brown and 1 wash of brown, 2 shades of green and one wash of green. Further for faces 2 shades of face collor and flesh wash and last but not least a metal collor (and if you want it fancy a black wash for the metal collor). So about 12 paints would be the basics I think.
An other tip I would give is to start with the 'real' thing. It motivates you more to do your best on the one model. And if you screw up you can always paint over it later or even start over all together after stripping away the paint. But do begin with the less important models so that when you get to the important models you already have some skill.
One last tip, start with a project and finnish it before buying new miniatures! It will save you a lot of money. I still have got some Lord of the Rings Models I need to paint... I have recently started painting those again to get in to the mood to paint the batman miniatures and the mythic battles pantheon miniatures. And read all the other comments there are some mighty good tips in there form far better painters than me.