Ace, Iam jelous. Thats a great looking
greenhouse. It might look good to have vines covering the metal too. What exactly do you mean by subterranean heating and cooling, how does that work?
For the weed blocker, upgrade to silt fabric. Erosion control and masonry suppliers carry it in 3' and 10' wide rolls around here. Its much thicker, longer lasting and effective.
For the beds, it really depends on what you can find or have sawn up for you thats the most economic. Looks like youre east coast so
locust, white oak, cedar or even hemlock could be good species. If youre doing a rough cut floor too then I may specify two floor beams with short 4' lengths at 2" thickness (2x6(or random)x 4'). That could reduce bending over height too. For the walls, butted 2x material with alternating corners held with structural screws. Would need to reduce to 16' lengths max I suspect and would need some collar tie type thing. Rough sawn 2x is the thinnest material I see being cost effective but going thicker would obviously be better.