Ok there are a number of things which can improve your gaming and make them worse.
1/ Make sure you are sitting up playing not too far from the TV, if you lean back or lay down i find you play alot worse even if you are fully concentrating.
2/ A pair of headphones certainly help, i have Turtle Beach X11s which are very cheap, currently $42 on Amazon. (they don't work on PS3 if thats what you own but im sure you can get a similar pair at similar value )
3/ Your thought process matters alot, your gun should be a big decision maker in your actions, for example if you know a guy is around a corner, and you have an Assault Rifle in particular an M16 or a gun with a slower fire rate, then wait for them to make the first move, and if you have a Sub-Machine Gun, and run around a corner you have to be quick and accurate (kinda obvious but to the point)
4/ Stick to the edges of maps and in high action zones walk around the corner whilst aiming your gun down the sight.
5/ Your perks make a big difference.
The only perks i ever run are
Flat Jacket Or Ghost Pro
Sleight of Hand Pro Sleight of Hand Pro
Ninja Pro. Hacker Pro
Reason Being, they work well together, i cannot play without Sleight of Hand Pro, which if your not using will really help you with your issue of feeling your not getting the 1st shot off, as it makes you aim down the sight quicker and reload quicker.
And the remaining 4 perks i find work best in pairs.
Flat Jacket and Ninja Pro
Reason being, a hell of alot of people have headphones nowdays and can tell where you are so ninja is very important but also ninja pro is as if you dont have ninja pro your guy still shouts things out which can easily be located with headphones, and as you dont have hacker it is best to run flat jacket as you cannot see claymores and it saves you alot from them and also from grenades and semtex you are almost invincible from them, unless your holding up a spot in domination and you get bombarded by like 3 or 4 at once which would be enough to kill you. (Flat Jacket Pro is not important)
Ghost Pro and Hacker Pro
Reason Being 2 words, motion senson (worst thing on the game by far) but hey if you get hacker pro its good for you because you don't show on theirs, and also with hacker pro their isn't much reason to have flat jacket as you would be able to see all equipment and not get killed by it. Ghost Pro is good for obvious reasons you don't show up on spy planes, and you have no crosshairs or name above your head, also you cannot be shot by helicopters.
I really would opt against using stupid perks like Marathon and Last Stand, as the two ways to stay alive in the game are too use Ninja against the guys with headphones and Hacker against the Motion Sensor campers. If you notice a team using alot of equipment use Hacker if you wear Hacker and feel they know where you are all the time then they prob have headphones and switch to Your Ninja class.
My typical class would be the above perks with, Famas-Suppressor, CZ75 Extended Mags, Frag, Stun Grenade and Motion Sensor (which i will very rarely even place in team death match ) mostly when im one on 2 etc in search and destroy to guard a spot.
Good Luck and let me know if you need a partner to play with and if you have xbox and need tips etc.