There's a walk buton, and if you ask me it is one of the most important buttons in the game. If you know an enemy is right around a corner, walk. WHEN IN DOUBT, WALK! -- it will save your life countless times.
Also, when you're climbing up a ladder, CROUCH and climb. It will make the noise of climbing the ladder almost silent and you are not slowed down. Experienced players will stand on a corner when they know the enemy is on the other side and wait to hear footsteps. Right when the enemy is about to turn the corner, you jump out and start firing as soon as you see him. This makes you more likely to get a headshot, considering you're above him. Excellent strategy for close range.
Most guns' recoil sends the bullets flying straight upwards. This is especially true for the SIG and the Colt M4A1. So if you're using those guns, fire two- or three-round bursts at the upper chest/shoulders of the enemy. Your recoil will go straight up and you'll get headshots all the time. After you do this for awhile you will develop enough accuracy to be able to automatically flick your mouse to that position whenever you see someone and they'll be dead in 2-3 shots. A lot of times on servers people always either ask me how I get so many headshots or accuse me of cheating. This is how. I always use colt.
As a general rule, double- and triple-tapping or bursting is the best strategy. With most guns, excepting maybe the smaller SMG's, they become incredibly innacurate after two or three successive shots. For instance, try full-auto'ing the AUG. It sprays EVERYWHERE. That's no good.
If you feel that you need to use more than two or three shots at a time, CROUCH. It lets you fire off an extra two or three shots without losing accuracy. If you see an enemy at long range, it's almost always best to crouch because it increases your accuracy just enough to kill him from all the way across Jeepathon.
I never buy Kevlar. I find that it's pointless, and a waste of my hard-earned money. Nightvision, on the other hand, can be very useful. For instance, in Militia. It's best, if you're a CT and you're taking the tunnel-route, to leave the lights off and catch the Terorists off guard. You won't be able to see anything unless you have Nightvision. There isn't many instances where it is useful, however. Only a select few.
As far as pistols go...I tend to like either the Desert Eagle or the Five-Seven (CT only). The DE is incredibly powerful, but it fires very slowly so you have to get the first shot on target or you'll be killed. The Five-Seven is incredibly fast and although it's not very powerful, you can run up to an enemy and STRAFE around them in a complete circle firing your Five-Seven and so long as you get tbhe majority of them on-target you'll have a clean kill.