Take things slow unless you have fantastic sightlines. Nasties have a tendency to pop up right around corners, and once they are spotted they get a move action IMEDIATELY. If you weren't prepared for that you may be left in a bad situation, especialy if they have alternative movement methods (jumping, flying, supa speed).
GRENADES ARE AWSOME early on. You get one use per soldier equiped with it, so try to hold off using them till you REALLY need to kill something right now and don't want to risk that rifle shot doing a measly 2 damage, OR if there are two or more enemies grouped together. I once got four floaters in one grenade toss, and it was the best thing ever.