I have a rough-in fireplace in basement and am considering finish it.
1) Should I build a masonry, wood burning, gas or electrical fireplace?
2) What is the standard firebox opening size? Should I buy a pre-fabricated fireplace before cutting the opening?

I believe I know how to figure out eh hearth dimension. Any suggestions for the mantel type/style?

Sounds like you should consult a brick mason.
I've never heard of a rough-in fireplace. You either have fireplace or you don't. Sounds like you have a masonry fireplace on an upper floor and what you have in the basement is its base. You can't just go cut a hole in it and make it a fireplace. The whole thing will fall down. Besides that, the base will probably be filled with rubble.

I agree with Harold. If you just have a cahse for a chiminey I'd consider a hig efficient gas unit, some do not even require venting at all. Tons of heat and no messy ashes or logs.