Getting a good distortion tone starts with gain staging. It may be hard to get a range of different distortion tones from Clean, Blues, Crunch, and Metal from one amp or pedal. But combining them together in stages using different blocks, models and tone adjustments can give you a lot of flexibility on the amount and color of distortion and sustain.
One thing that's important is to use the least amount of distortion (effects, etc.) you need for the song. This makes things simpler, produces the best tone, and gives you a place to go in the next song. Music needs space.
Start with your desired clean sound, using the neck pickup on your guitar with the guitar volume and tone all the way up. This is your inital, set point amp tone and something you'll need to be able to go back to. Once this tone is right you'll probably notice that it's too bright for the bridge pickup, creating too much edge, or an "ice pick" tone that unpleasant after listening for a while. Don't change the amp to fix this since that would break your neck pickup tone. Instead roll back the tone control on your guitar to warm up the bridge pickup a little. A lot of people never touch the tone controls on the guitar, or only use them for slide. But the bridge pickup tone control is actually pretty useful.
Next add a gain stage for warm, just on the edge of breakup, Blues distortion tones. As distortion increases, base has to be cut to prevent a muddy, indistinct sound that competes with the bass player, and treble needs to be cut to avoid fizz, buzz and ice pick. But since a Blues tone isn't that much distortion, you can often get this from the Drive control on the amp. Assign a footswitch to the Drive control and assign a controller to set the min (clean) and max (blues) Drive distortion levels. In this case, the drive is increased to add some amp distortion without changing the tone. Be careful to minimize the amount of distortion or it will get muddy and bright quick.
For a Cruch sound, you'll need a bit more distortion, which will require some base and treble cut. I like to use the Studio Tube Pre for this as it adds a nice tone of its own, and has the Drive control for increased distortion and the low cut and high cut you need to adjust the tone. Use the Sensitivity control to adjust the amount of distortion that can be produced by the Studio Tube Pre. Set Sensitivity to Mic for greater distortion, Line for cleaner tones (the Drive can be set higher without adding any distortion). I use Mic for this application as I want more distortion.
Other options for Crunch: Valve Driver, Minotar, or ProCo Rat. I know the ProCo Rat is intended for high distortion levels, but it actually cleans up very well by turning the drive down and adjusting the filter for the desired high end. I think this block increase bass cut with increased drive, which is just what you want.
For Metal or more agressive tones, I like Compulsive Drive (Fulton OCD). Screamer works well too. Use the tone control to adjust the high end. If it gets too muddy, try adding a Low and High cut EQ filter in front of the distortion, and link the low cut to the distortion footswitch to cut closer to 80 Hz when the distortion is off, 160 Hz when it's on.
Now you have four distortion levels, all off for Clean, and each block on/off for Blues, Crunch, Metal. Now you can start combining stages to get even more tones. For example, I like to combine Blues and Crunch together for a more aggressive blues solo.