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squats are a good start, but there are many components of strength that would need to be worked on. Start with your biggest bang for your buck compound lifts and most importantly practice

I am working on everything to be as strong as possible.  This question was for curiosity's sake lol. 

I am a basketball player so I just wanted to see if you guys knew which muscles are used and need to be strong (don't say all, tell me which one's are more primary and more emphasized) in order to be good at the following:

1) backing someone down (posting up)
2) guarding a post player (not letting him back you down)
3) first step quickness (crossovers, blowing by defenders with the ball cuz your too quick)
4) lateral quickness (to stay in front of your man on defense)
5) jumpshooting
6) when driving in, absorbing and taking contact from your defender
7) defending your guy driving in on you with body contact (opposite of no.6)
taking contact during a lay up when you put your body into there big man
9) boxing out
10) strong cuts

Sorry for long list but if people who know their stuff can just answer them in 1-10 format that would be great

if you really want to know, find a kinesiology manual online or something, but there's a problem with your line of thinking.. if you dissect all of those movements to the exact muscle groups, you'll start thinking in isolation.. bottom line, have to get strong everywhere, especially the lower body.. me or anyone else with kinesiology background on here could dissect it into the various muscle actions & thus which muscle groups but it would be futile hehe.

as for taking contact, thats your body just getting smashed, you'll want added lean muscle to help you in the 'weight department'.. nothing would be better than 'fat' for absorbing contact but that obviously wouldn't be a good answer here.. look at a guy like lebron or baron davis, very strong going to the rim -> lots of lean mass, lots of power driving to the hoop, people bounce off of them..

pc

No, but really, literally all of the numbers you listed up there will be helped greatly by squatting.