Again, welcome to the forum!
Well as a traditional artist, i’m sure you have the basic needs of a matte painter; a good understanding of lighting and composition.
On the technical side you going to need a mid level wacom tablet, something like an intuos 3 is ideal, anything more is just bells and whistles 
You can pick up a few on ebay.
Put together a good PC or Mac, many will argue one or the other but either will do fine for running the essentials. A good graphics card, most gaming cards will be good, but one in the quadro range will be more suited to vfx needs.
A dual monitor setup is a good investment, the bigger and more expensive monitors you can afford the better. Always good to be able to maximise your work area.
And one piece of equipment that often goes overlooked but one that can really make or break your work, a comfortable seat to park your butt on! Never under estimate how much your working environment can effect your work
As for programs, well lets see, photoshop is the essential and must have, this is where most digital artists will spend most of his waking day. I wouldn’t recommend Painter for matte painting, its a great program for concept art and simulating traditional painting, but for matte painting this just encourages bad habbits. Once the painting is finished and you want to begin bringing things to life, you might want to invest in a program like after effects, from there you can start adding little effects like smoke, moving clouds, creating simple camera moves to add depth, that kind of thing.
When you come to the point of wanting to add more advance animation you need to start moving into the 3d world; cinema 4d is a good 3d program that is very much designed towards photoshop users with great tools for turning matte paintings into moving environments.
To add to the above, you could also use an external hard drive for storing reference pictures, stock footage, textures etc. Every matte painter should have an extensive library of references It;s worth noting that matte painting is less paint and more photo manipulation today.
Stock footage is always handy to have for bringing shots to life, http://www.videocopilot.net/products/action2/ is a good one.
A good digital SLR is also a good investment. Add to that a HD recorder.
As for training, the internet is lacking somewhat in training material for matte painters. However there’s a few kicking around. Take a look through some of the free videos on this website: http://www.videocopilot.net/tutorials/ you’ll find a few environment related tutorials in there. Then there’s gnomon workshop that is the leader in vfx training material, with a number of matte painting related dvds. http://www.thegnomonworkshop.com/
Well thats a pretty good list to keep you going. Second to all that, just look at peoples work and ask questions
good luck
Dave.
