When painting its useful to Bluetack your miniature to an old paint pot so you can hold it firmly without ruining the parts you've already painted. Its also a lot easier to handle.
I think the choice of brush and paint makes a major impact on both your painting style and the results you achieve. Decent brushes make a real difference but can be a bit expensive. Try your local Hobby or Art Supplies store, but don't discount your local Games Workshop store, their brushes are actually pretty good and very well priced. I tend to spend about £5 on a good Sable/Synthetic mix brush but the Games Workshop ones are certainly good enough and only cost £3 each.
I tend to use a Size 1 brush for large areas of base coats and indiscriminate washes. Size 0 for most other things and a Size 000 for detail. You can use smaller brushes but my eyesight without a magnifying lamp isn't good enough so its not worth it for me. Bear in mind i'm not painting for competition or display but for models that will be well used by 6-7 people on a weekly basis.
Eventually your brushes will start to droop, split or get generally a bit tired, don't put off replacing them but keep the old ones for dry brushing. Nothing ruins a good brush as much as dry brushing in my experience. Its a great technique and I use it a lot but it'll kill your detail brushes dead!
Now on the subject of paint. I have quite a lot of Games Workshop's Citadel paint, its really good quality, pretty consistent and the colours are bright and vibrant which suits my style quite well. But they are expensive and quite thick. You also lose some to drying out in the cap when you paint as the pot is open most of the time your using it.
The alternatives are generic hobby acrylic which is well worth trying out, especially the base colours you lose a lot like black, white & the primaries. At £1.25-£1.99 each for nearly three times the amount you get from Games Workshop its a no brainer!
Now there is an alternative paint supplier that i've just started trying out. Vallejo paints. First impressions are that they are excellent. Thinner than Games Workshop so flow better, you get more in the bottle and don't lose as much as you just squeeze out a small blob onto your palette. You can get a plastic or ceramic palette from your local Art Supplies Store (or WH Smiths if your in the UK) and they are excellent, much better than using a normal dinner plate. As an added bonus your nearest and dearest won't want to kill you for painting all over their cherished Pricess Di comemerative plate either.