You basically need ATLEAST 2 classes specifically for Search and Destroy.
The first should be silenced weapons + Ninja, the second should be the same (or similar) but with Cold Blooded as well as Ninja. This is so that if they call in a UAV at the start of a round you can quickly change.
Normally I use Marathon + Lightweight, not too many people use this in S&D for some reason so you should be able to get into position for either camping or rushing.
For equipment I would go for Claymores but frags or semtex do work as well.
Offense can be hard, normally I rush to about half way and take it easy, listen out for footsteps etc and only plant when its safe (or camp/defend when it is planted).
Defense is a lot easier than offense, usually you are closer to the bomb sites!
The key to Defense is knowing the map well, knowing where the enemy will typically go and then having half a dozen spots to camp. Yes... camp!
S&D can really be a game of patience, sometimes just lying prone and being very still will get you kills as people will often just run past and not notice.
Killstreak setup should be UAV, Care Package/Counter UAV & Predator Missle.