Unless you rectify the water issues in construction aspects of the porch itself, the sustainability, longevity, and maintenance of any flooring flooring system and associated area construction will be in question (just like your wood floor and columns)unless you choose a system specifically made for an exterior application. With your porch in its current state, what comes to mind is a ceramic/stone solution made for an exterior application with membrane over mud-bed over menbrane construction and a drainage/gutter/flashing system (like at least Schluter Ditra/Kerdi or even better Troba/TrobaPlus with a BARA/BARIN drainage/gutter systems for porch/terrace/deck systems). as for tile product choices, a high quality porcelain is an excellent choice for decorative exterior applications. a high grade masonry sealer for the joints is advisable as well. The important thing here is to either: (1) fix the water coming in, or (2) use a system where water penetration is irrelevent. Please dont make the mistake of simply installing cement board and tile over the wood substrate to save costs. While it may last longer than the wood, you will still most likely get water penetration into the wood subfloor/framing system, which in time, will still deteriorate the underlying wood, eventually causing tile/backer board system failure. Nothing will last over a wood subfloor system over wood framing if you dont take the proper precautions. Here is a link that might be useful: Schluter Systems

Depends how much you want to spend---but I'm having a screened porch built now to replace the old one that was just torn down. We get a little moisture but like you, it doesn't get drenched inside. Our contractor is using a thick tongue and groove pressure treated flooring and will stain it with Sikkens to be a cedar color. That was a cost effective option that looks good and since it's tongue and groove, we won't get bugs coming up through the floor and we don't need to screen under it. We're using a composite for the adjoining exterior deck---Fiberon Professional Series in brown. I think if you have more to spend, you can get something that's an upgrade, such as cedar or a hardwood.

I re-read your question; you have heated/insulated rooms below a porch. Therefore, the wooden decking has no air movement underneath it, so it can never fully dry after rains. Any rain is able to penetrate through the many seams in the flooring and get the insulation and framing wet, and they can't dry out either. You need to understand the construction details that are necessary for this situation. It consists of building a seamless flat roof, that is impermeable and drains water away from the house, then building a walking deck on top of it. I have done three projects like this. The first one. we used a torch-down adhesive roll roofing, then 2x4 floating sleepers and a 3/4" traditional wood flooring. Second one, a subcontractor put down a EPDM rubber roof (we had to tear off everything because the old rubber roof failed and ruined the decking and a lot of the framing) then we built modular, removable hardwood duck boards that fit into the space and were removable for cleaning underneath. Third one, the metal roofer came in and built a flat copper roof, and we did a normal porch floor on sleepers as in #1, but this time in mahogany (more stable and rot proof) , painted. I just wanted to point out that there are more issues in play than you may realize, and your path forward is not simply choosing the most maintenance-free finishes. Casey

The largest heater you can buy that you can plug into a standard 120 V outlet is 1500 Watts. That is about 5000 BTUs of heat. That should be enough for 58.5 square feet, but you do have a lot of glass on three sides. If you are facing south or west you will be comfortable on a sunny day. A very cold night might be a problem. Amazon has dozens of heaters of all types. Read the reviews and see what you like. Most if not all have a safety tip over feature. They are supposed to shut off if the dog tips the heater. You also buy a wall mount type if there is any concern. It would also free up space for furniture.