I've fought with my Mark III for years, and I'm only just getting to the point where I think I've mastered it and have a superb clean, crunch and lead tone. Here are a few of the paths and diversions I've taken over the years.
btw, mine is a 60w red stripe with reverb and without EQ, 1X12 celestion Black Shadow. I use a strat with texas specials and a Jeff Beck strat (and occassionally a Ricky 12 string). The amp is tubed with JJs
First, the EQ: I bought an MXR 7 band EQ pedal years ago because I had EQ envy, but I don't even plug it in anymore. The V shape sounds great if you're playing metal or playing solo at bedroom volume, but I found that as soon as I was playing with a band, the sound just dissapeared. I imagine the onboard EQ is similar, but it certainly makes the amp more versatile. If you don't like it you can leave it off.
Mods: When I first got my Mark III 5 or 6 years ago, it had an annoying buzz when the reverb was turned up. I found a simple mod on the net that got rid of the buzz and made the reverb sound overall better.
Also I did the very simple R2 channel master mod to balance the levels a bit better between channels.
Attenuator: This made the most dramatic difference. As everyone knows, Mark series amps are very loud. They also have a sweet spot on the master volume at about half way, which is WAY too loud for most use. Above this, the master just adds compression and crunch, not volume. I bought a Weber MiniMass and use that as my master volume, and leave the amp's volume on 5. It gives a great sound at bedroom levels, and at band volume the sound just leaps out.
Presence and treble: Sometimes I think they should have left all the other knobs off the amp apart from these two, because they have by far the biggest impact on sound. With my strats, I run the treble low (around 4-5) and the presence about the same. There are some wonderful spanky clean sounds to be had with the presence up high, but for overall balance between channels I keep it low.
The way I have the amp set, the clean channel is smooth and slightly overdriven, sort of like classic period Stones and perfect for clean Hendrix. The crunch channel sounds for all the world like a great Marshall, or even HiWatt. With a bit of delay it could be straight off the Who's Live at Leeds. The lead channel is just classic smooth Boogie, with a bit of bite.
Over the years I've gone through cycles of loving and becoming frustrated with this amp, but when set up right, it blows all my other amps away (present and past including oranges, Marshalls, a VHT, Fenders and other Boogies).
Another point, the amp can sound boxy and midrangy when played solo, especially at lowish volumes (which is why the EQ often helps). Put in a band mix, however, it has just the right frequencies to sit properly in the mix.
Hope this helps