Kind of hard to say exactly what's going on there, but I can say what's worked for me so far. The first thing I'd say to do would be to go into options and turn on "Traditional Sculptris navigation". It would mean getting used to a slightly different control method, but being new to Sculptris you shouldn't have too many habits to relearn and it would also stop the movement of the model while you were sculpting on it unless you were holding down the "alt" button or the middle mouse button to move and rotate. I'm probably one of the few who still use the original navigation and wish ZBrush would adopt that control method rather than adding their controls to Sculptris.
The tablet/mouse debate has gone on for quite a while, but in my opinion, it's still just a tool. Neither is better than the other. The main thing that matters is what you feel most comfortable with. I personally use a mouse, but it's what I'm most comfortable using. I can use a pencil, pen, or paintbrush, but I just can't seem to get used to one of those tablet pens...
Just like anything, it's all about practice. Like MentalFrog was saying, Sculptris is just a tool in itself to get used to. But, once you get used to it, it's probably the easiest of all the programs to quickly get an idea out there without having to worry about all the rest of the usual 3D roadblocks.