s0c9 has you off to a great start. Just scratching the surface, but I can tell you a few amp "tweaks" that I play with.
The "B+constant" is one of my go-to tweaks in the Axe-FX II, especially for hard rock/metal stuff. I'll normally bump that up to about "45" or so. It adds a definition and clarity that is great for doing "galloping", etc. riffs (think Megadeth) but would be great for all kinds of music, etc.
If you want to add that low end "feel" that is not just turning up the bass knob, then mess with "depth". This control is hard to even put into words but for me, it gives an amp that low end wallop you hear live. When I was previously playing into my Marshall 4x12s and felt I was lacking low end, I could turn that and instantly get a low grind.
"Bright Cap" is a great way to adjust how crisp and trebly your amp sounds. If you want "bright" on, but think it is too overwhelming, this is a great adjustment.
I don't understand a lot about "Triode Plate Frequency" but if I remember correctly, I turned down the triode frequencies on Triode1 and Triode2 to capture an early Van Halen tone. Maybe someone can explain why that is.
"Amp Voicing". The "Modern" setting is great for almost any heavier tone in my opinion. Just instantly gets that hard rock/metal tone.
I never wrote down my settings, etc. but back when I was trying to capture a great early Van Halen tone, I think I brought the power amp tube values up and dropped the preamp tubes a bit.
Whenever I'm messing around with amps (granted I don't know a lot about the insides of a tube amp), I try to think about the time period and player. For example, I know that Randy Rhoads, Tony Iommi, Pete Townsend, etc. had to depend on a pushed amp to get their tone and a lot of volume. I keep that thought in my head while I'm tweaking and will even go online and try to read about exactly what setup they had, etc. I think it is important to read about what these players were using in the studio, especially now that Cliff has these amps so close to emulating the originals.
Again, this is just my opinion and scratching the surface. I never would have figured these things out had I used Axe-Edit all the time. By forcing myself to mess with the front panel, I really started learning more about tube interaction, etc.