You have LOTS going on here.
If you were to heat a wall in a basement that's UNinsulated, you'll end up w/condensation problems. Hence, as you already know, you need to finish the walls. You'll need to stud-out the wall and insulate. Of course, you'll need electrical and such too. Your best bet is to find a book at, say, Amazon.com or some place that tell you how to finish a basement. Sometimes, these books are 'lumped' in with finishing an attic. There's too much to consider here for me to write. I do recommend a pressure-treated lumber for the baseplate, and foam board insulation.
Forget using a ventless fireplace. In my optinion, they simply dump too much moisture into the house. Water is a natural by-product of combustion of natural gas, or the like. Just plan on venting it outside. I will say that, depending on how you will use your basement, THAT'S how you should decide how to heat/cool it. If, for example, it's a family room that gets lots of heat, a vented fireplace would be nice. If, however, it's only used for storage or for rare occassions when too many 'kids' come to visit, electric baseboard heat may be better.
I don't know what you mean when you say, "Run venting to floor level." You should finish off the room as you would any other room. There are code issues. For flooring, I suggest a Berber-type carpeting. You'll need to determine if you have a moisture problem now BEFORE you do any work.
Lots going on here. Spend a few $$$ and buy a good book on the subject. My best to ya and hope this helps.
Jay J -Moderator
PS: God Bless America!