OK, my memory may be a little misty 'cause i played this game quite some time ago. But i will share my strategies the way i remember them.
A) The most probable way to die in this game is to run out of ammo. To solve this problem, go to storage tower immediatly after the beginning of the game (it's just north of the civilian tower, where you begin). Stay there until you get a shotgun and possibly a magnum.
B) The goal of the game is to kill the queen; to do so, you will need some heavy firepower to get rid of the elites around her. Queen herself is no weakling, either. Smartgun is my weapon of choice here, with at least 50 units of ammo. Military tower is the place to find this toy, and possibly a power armor (the tower is west of storage tower).
C) Speaking of Elites. Those bastards are sure to spoil your picnic, so anti-elite measures are a must. Krak granades can kill them in one hit. Plasma rifle is good here, too. If you don't have this weapons, magnum can save the day. Failing that, the starting equipment can sort 'em out with a few medpacks. Just don't use your shotgun, it can't punch through elite's armor.
D) Watch out for randomly spawning hunters. They hurt. A lot.
E) If you have the ability, explore as much as you can. It gives major exp bonuses.
F) Draw the maps of the levels, especially note where the lifts are. You'll need them on your way out. I failed my game twice because i didn't know where those damn lifts are.
G) About classes: i found out that the scout works the best for me. But any class except medic and the tech guy (forgot the proper name) will do, really.
H) The most important note: DO NOT PRESS CTRL C! NEVER DO THAT. You don't want to end up losing your game after hours of playtime.
That is all. I belive i left a video of of one of my runs in the video topic. It's long and boring and full of me doing stupid things, but it does illustrate some of my points.
PS: Have you noticed that the corresponding up and down elevators spawn on different parts of the floors. Say an up elevator is in the NW part of the floor, but if you take it up you and up in the NE part of the next floor. So if the elevators in the year 2200 are the same as our elevators, than the towers should look like this:
(XXXXX)
(XXXXX)
(XXXXX)
(XXXXX)
(XXXXX)
from the outside. Which is silly.