Hello Holly:
I would definately try to steer you to traditional oils over any other system. Real oils work better, feel better under the brush, and will certainly last longer, IMO.
M.Graham paints are nice. I have several tubes. I can also recommend most of the other primary manufacturers like Old Holland, Gamblin, Vasari, Rembrandt, even Utrecht! Further, there are a number of small manufacturers out there who make excellent oil paint - Doak, Ozog, and Harding are two examples.
As for solvents, you certainly can paint without them. I use OMS to clean my brushes and my palette. I use Oil of Spike Lavendar to actually thin paint which I don't do very often. Spike is also a solvent and has a nice smell.
As for drying your paintings, you have two options - wait for them to dry naturally, or add some sort of drier to your paint.
Driers are typically composed of some sort of metal - Cobalt, Manganese, and Lead being the primary ones. I use and very much enjoy Lead White (Flake). I also use a painting medium which has lead in it called Maroger. It is nice stuff. Lead has the advantage of drying the paint layer throughout where as the others dry from the top in.
A medium can serve several purposes. You can add a medium to your paint to help the paint to handle better, and as I mentioned above, mediums often have driers in them. The rule about painting medium is "less is more". Use them sparingly and I advise that you test test test to find what works best for you and how you paint.
Try everything once and make your own judgement.
