Sheetrock does have some fire-retardant properties, but it's a little tricky for one person to install alone unless you have both
experience and some special equipment (the equipment can be rented, usually -- you'll need a lift to get the sheetrock up for the ceiling). Personally, I'd just as soon put
wood boards on the walls and ceiling. They don't need to be painted (I've been painting here today, and wishing it wasn't necessary, LOL!), look nice (in my own home, I would treat the wood in such a way that it wouldn't darken too much, as I like light in my living areas), and are much easier to put up by yourself than 4' X 8' pieces of sheetrock!
Alternatively, you could put up lathe and do plaster. It would be more work. Don't know how the price compares, but I suspect when hiring it done, labor is most of the cost. Well done plaster looks really nice, and would be at least as fireproof as sheetrock. Needs white-washed or painted, though.
Kathleen