You can do radiant under wood floors, you jsut operate it at lower tempratures. But in a cooling dominante "green grass" climate like Atlanta area, I don't think it would be worth it sie your heating season is so short.
If it takes a GC or drywallers 6 hours to cut and repair the wall, you money ahead if you spend about 2 fewer hours installing the furnace.
Bathrooms OTOH are great to have heated tile floors year round for comfort. But since they are small, it usually most economical just to use electric.
Yes... in Atlanta a HP is not always the best approach... mainly because when we DO have those really COLD nights (well cold for here)... recovery is slow unless one lets the Elec strips take over... then the elec meter spins like a Frisbee...
I would vote for gas furnace and 16 SEER (2 stage) AC. I would also vote to carefully evaluate the ductwork (as with all jobs). Most duct systems are grossly wrong... and hanging new equipment on bad ducts... well it is at best a WASTE of $$$... and at worst a sign of a non-professional contractor. I have literally walked away from a few jobs because I KNEW what would happen if we did not address the ductwork.
Also; IMO with a house as large as the OP's (original poster); I would invest the $$$ for a thorough energy audit. Get someone who is either BPI or RESNET certified... and let them go through the whole house... it will probably take the better part of the day. Believe me; there is a LOT more to a healthy and tight house than foaming the rafters, installing new windows, and caulking. Hire a PRO to do a PRO's work, and one gets PROFESSIONAL results...
Back on basement systems: I did one a few summers ago... guy has a computer business he runs out of his basement. Had half/dozen servers in a closet, two offices and a great-room. We set him up with gas heat and AC... AC was a little over-sized on purpose (keep the servers cool), and 2 stage... worked like a champ!
As always, I was on the job during the install... I had my guys CAREFULLY cut out each hole in the ceiling so the piece of drywall could be replaced in the hole (and the hole was cut along ceiling joists). I put the pieces back in the holes when I was done. Customer hired a drywall guy who cleaned up the joints and made the access holes literally vanish! Basement needed painting anyway... so it worked out.
I also remember a house I went to last year... Guy had hired a CraigsList hack to do a job similar to what I described in the previous paragraph... you can guess the results. And as always happens with a cheap contractor: Their phone was not in service a few weeks later. I explained to the guy what was needed... he liked to had a coronary right there when he realized it was gonna cost him MORE to fix it than it cost to install it... including holes and painting AGAIN! Shame... guy did not do the repair... he got a couple of window shakers... Shame... it looks like... well... nevermind.
Galatians 2:20-21; Colossians 1: 21-22 & 26-27; 3:1-4; Romans Ch's 5-6-7-8
2 Chronicles 7:14
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