custody and child support questions??

Paulina
So I really want to get either full custody of my daughter or (is this part of joint custody idk much about this) get it to where if my ex wants to see her that the visit has to be supervised as he did threaten to harm her before she was born and while I'd be welcoming to his change of mind about her I wouldn't fully trust him for that word to be genuine... 
However I also want to file for child support .. And please don't say I'm being lazy or looking for a handout because I want CS... 
I just want to be able to give her the best and I honestly think the bit of help it would give would make a huge difference...
Anyways my question is if I were to get full custody so he couldn't see her would I still be able to get child support? Or would he no longer have to pay since he doesn't get to see her?