I also use artists paints, and well I'm a golden fanboy, though lascaux are creeping into my palette more and more. Einion and I disagree on the best paints (which is as much as matter of price and taste as anything else there are many good choices), but he is right about the advantages and pitfalls associated with any artists paints. Though I confess I also disagree on the relative cost difference, GW paints are hugely expensive for value, in my opinion. While it is true artists colors are more expensive, they give you more paint, so cost per ml is pretty close, if you shop right (and blick is a good place to start). One line i would consider is lascaux studio, they won't break the bank, and they dry to a beautiful satin (though I would stay away from their metals, the pigments are ground too large).
With artists paints, you have to really love the process, because they are more work. I use some additives to acrylics, mostly to deal with glazes and washes, but thinning with water works well. I have used both retarder and open acrylics and find that they don't make wet blending that much easier, but if you are learning these techniques and investment in a drying retardent is not a bad idea.
I think a wet palette is and essential tool in all painting (every golden demon winner I know uses one) but it is even more essential if you are going to use artists paints. Half the joy of using these paints for me comes from the fact that I am forced to mix and explore color. I like vallejo paints just fine, and reaper and foundry, but I found when i was using them, I got a little "paint by numbers" in my approach. Not that this is bad, but it was not fun for me. So the transition to artists colors made me think about mixing, and also forced me to learn color theory, which was probably more helpful in improving painting.
Now I am moving into oils, at least in the for of oil washes and I am again amazed I did not try this sort of thing earlier. I can match the oil's fluidity using acrylics and additives, but I cannot match the oil's ability to be taken up. Being familiar with artists brands I tend to use those (mostly williamsburg and old holland) but I am told the MIG Productions Abeitlung 502 (or somthing like that) are terrific paints. With oils more than acrylics, I would avoid the cheaper brands.
I think an airbrush is essential for a lot of reasons. One less obvious one is the ability to lay thin coats of varnish as you work on the figure without losing detail. This mean you can gloss coat before you apply a wash (or washes) and then put a matt coat over that to continue painting. Again this is just a hidden use, there are tons of interesting stuff that can be done with an airbrush.
One thing to think about when getting paints, its that red, yellow and blue are not really the primary colors you want to mix with. You want to invest in a Magenta, a Cyan, and yellow, preferebly in a non mineral pigment, and mixing these will produce much less frustrating results. I say this because its easy to see a cadmium red or an ultramarine (or cobalt) blue and be taken in by the intensity. this is a good thing, but these are not good colors to mix with.
Other than that, all I can say is explore and enjoy. There are not really a lot of wrong answers with painting, but there is a lot of trial and practice involved.
. I currently only own a few oils, mainly some browns and lighter fleshy colors. I use them as glazes primarily ad then take a hairdryer to them. I do make sure to use plenty of ventilation on them and they do stink, haha.