What fuels can turbofans burn?
As explained in Why do jet engines use kerosene rather than gasoline?, turbines can burn almost anything, but the lubricating properties of kerosene make the fuel pump simpler as it is otherwise hard to keep high-pressure pump lubricated.

Temperature limiting is simply a matter of sufficiently lean mixture and cooling air stream along the combustor walls.

And most efficient depends on criteria. For money it is definitely kerosene (Jet-A). Actually, Jet-A is an excellent match overall. It is relatively dense (~0.8 kg/l) while still having good specific energy (~43 MJ/kg; so fuels tanks are not too big), lubricates (good for fuel pumps), has quite high flash point (low risk of fire when handling) and is a large fraction of crude oil (C8–C16 (gasoline is just C6–C8) so it is cheap).