I recently purchased an older home without a fire door between the garage (which contains the furnace) and living area. I'd like to install a proper fire door but I'm not clear on whether it would be sufficient to hang a door on the existing wood frame or if a new (metal?) frame would be need to be installed as well. Hoping someone here might know. Thanks in advance.

There are interior doors made for sound reduction, they have STC ratings and there are exterior doors that have STC ratings you could compare the numbers to each and compare them to your wall assembly and see what would work. 1 3/8 interior doors can have a better STC rating than The wall. You could retrofit a wood threshold to the existing door to close the gap at the bottom or just lower the door assembly if it is on carpet and use the carpet as a friction fit . If your dead set on on an exterior door you remove the threshold , cut it down and modify if with wood and also shorten the width, you could remove the aluminum sill, cut the frame down and put a lower profile sill in or let the weatherstripping graze the floor.. If you like the aluminum sill just replace your flooring with aluminum flooring to match the threshold. There are many options but lack of details to help assist.

Don't bother with FG. They are much longer on the lead times. Provia makes a good door and anything there should last.

That seems a questionable call. We are required to do that on our current build if it is to be a legal two-unit building. A commercial specialty door manufacturer can provide the required door.