I have a lot of experience with this as I have done a number of my own remodeling projects, most recently opening a wall up for just this purpose. Any estimates given without knowing whether or not it's a load bearing wall, whether you simply wanted to cut a window like opening in the wall, or open floor to ceiling is not worth much.
That said, if you want to keep costs down and get more light and open feeling the best way is to cut an opening like a window because all you need do is add an extra stud and a header, but keep in mind it could get expensive if you do with permits because they'll likely want an engineer involved.. If you want a real estimate, contact some local contractors - local agents should be able to give you referrals - and get some real world bids.
You might also open a hole in the sheet rock from one side so the contractors can see what's going on underneath.
Lance King/Owner-Managing Broker
King Realty Group