Welcome to the board!
What you want isn't difficult to get. More often than not, simply backing off the volume control a couple notches on just about any pickup will clean/clear it up without really lowering the output much, and you can get articulate/spooky from there. Crank it back up to overdrive the amp a bit, and you get the crunchiness. Depending where you want to go, there are about eleventy bajillion overdrive/distortion pedals you can place between the guitar and amp to force the issue.
As far as "cutting through the mix" goes, that's less your guitar and more your amp and/or FOH operator. Knowing that the drums and cymbals are going to dominate the very low/high frequencies, the bass is gonna want the low/mid-low freqs, and the vocals are pretty midrangy, you have to occupy the leftover space in the mids for your guitar to be heard. It sounds bad on its own - you probably wouldn't practice by yourself set up that way - but good with everybody else.