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

Floor and porch enamel is usually what works best.

Thank you so much for taking the time to answer. Our contractor seems to feel we couldn't install without a wall behind :( I will pass along this info, though, because I think the woodstove folks said that as long as you meet the clearance, it wouldnt' be a problem! So good to know they are holding up well and you get to use your stove a lot! Are you able to sit out there even during some winter months?

We had somewhat of the same problem. We decided just to put siding inside and out on that section. Besides it gave us a little privacy from the neighbors. Sorry my pictures aren’t very good, but it might give you some idea.