The easier of the two is that when presented with a difficult environment, you want to avoid exciting that space with frequencies that decay slowly.
I agree wholeheartely, and there's Lots of advice after that about what to do when hearing yourself through your amp, which is all good. I'll just add that the ultimate solution to being able to hear yourself really well is to go in ear and ampless. That way, the only source adding low frequencies to the space is the PA - that helps the house sound good. For you, having only what you want in your ears is a great thing, provided you can get a good mix.
Although it shouldn't have surprised me, a couple months ago I was located in the middle of a huge stage, well away from the drummer (Actually, there was noone within 20 feet of me - it was a bit lonely out there) At first, being 40 feet from the drummer seemed like a bad idea, but since I could hear myself well, and with the right mix, I could hear him clearly, not having the wash from the drums being next to me actually made it easier to keep he and I synced up. Eye contact was a bit more difficult, but not as much of an issue as I would have thought, and the whole thing flat out worked. It takes all the right conditions for this to work, but if you have those, it can be fabulous.