Welcome, the Mark III is a great amp (I've owned five hahaha.) Regardless of what style you're into, here's some dialin tips:
Treble = gain
Mid past noon = also gain
Bass: VERY rare that you'll want the bass past about 9 o'clock, though there's some interesting sounds to be had by giving it more bass at the front and then cutting it with the GEQ.
The pull knobs for treble and bass shift are pretty guitar-dependent, you'll probably like treble shift with an LP and not so much with a strat-style. Deep is mainly for single-coil sounds.
The GEQ is usually the key to satisfaction.
By modern standards the Mark III is a one-channel amp with lots of options. It's very hard to get multiple good tones without touching knobs. You can get a great clean and decent crunch by using the GEQ to pull bass out of your crunch, and a good crunch and high-gain lead by using Lead Volume and the GEQ to scoop one or the other a little bit (do not fear the scoop, the Mark III core tone has mids for days.)
Finally, the Mark III is a great, great studio amp, it sits in mixes beautifully and needs very little post-EQ.