My experience with live rock is that you can't fit that into this budget. You could probably do the rest for that amount--you'd need a good skimmer, (I'm not sure what carbon rock is?), and you wouldn't need a ton of live sand...you could mix it with some normal aragonite or sand.
I wouldn't skip live rock, but price for you is prolly going to be a problem. It depends on how much you want. Theoretically, you want 90 pounds, and you want good quality because that's partially the point of live rock...to have as much stuff living on and in it as you can. So even if you can find a good source in driving distance (shipping is at least $100 and it's better for the rock to not ship at all), you can still expect to pay roughly $4 a pound...at 90 pounds, that's $360, without shipping! "Uncured" rock may be okay, but you have to cure it and I'm not sure how low that drives the price, maybe to $2 a pound? I've heard endless horror stories about cheap rock, maybe someone here would have good advice though.
Anyway, my point...your components are prolly going to run you the $200, and maybe if you work creatively you can pick up enough adequate live rock on the cheap, but...if you do it the "recommended" way, you can expect your rock to easily cost you more than the $2-300 discussed all by itself.
rusty