Avenger armed with laser-cannons. I know it doesn't look exactly like it, but I always preferred the version found in the adds, thinking it looked way cooler than the one in the game.
When I dicover a Floater-base, I usually leave it alone and wait for the supplyships to come. As the supplyship land I attack it to get my greedy hands on their Elerium.
In most of the games I have played, the aliens seems to split the earth into areas. So that Snakemen keep to one area and Floater to another area. In my last game missions in Europe was always against Sectoids. I bet they do the rock-paper-scissors to decide who gets what