Room Question

Thick carpet with thick underlay is absolutely the best! The shortest dimension is usually the height. A carpet is absolutely the most important thing in any room.If you can't do at least a third to half the room in carpet then get a big rug and roll it out when you listen.

Depends on your room dimensions. I would either go for wall to wall carpet or hardwood floor plus high quality (wool?) area rugs.

A lot depends on shape of room and if you have other room treatments.

room is 14ft wide and 21 long. 8 feet ceilings.

If you have to redo the whole floor, it might be a good time to experiment. Mike Lavigne (Siriusly, the room's the thing!) has a great room with woodfloor in the speaker area, and carpet in the rest of the room: the closest reproduction to a concert hall. Sounds pretty good... (of course, there's a lot of acoustic treatment as well in his room!).
You could try something like that first, and then add carpet to the speaker area and test the difference. Your room has nice dimensions! Good luck.