diy

the gold standard for plastic on frame is 6 "mil" aka 6 mm thick clear polyethylene film "greenhouse plastic sheeting" for something that small, I would look at a series of removeable clips to fasten it and unfasten/remove at the end of season. plastic gets holes and eventually degrades in the sun after a number of years.

for fastening, in the states we have a product lovingly referred to as "wiggle wire" that uses a precisely pre-bent stiff wire along a metal tracking to hold plastic into place. I think they make smaller gauges for smaller houses like that, because the stuff I have used would be overkill. and really, your project is small enough that like a box of those heavy duty binder clips from an office supply store would probably work. I would make the back+sides more or less "permanent" and make the front be made to easily open/seal for access, watering, and venting on bright sunny warmish days.

edit: this is what I am picturing when I say binder clip, but really once you get the material and get a feel for its durability, you will know what will work. 6mil poly is no joke. like I wouldn't puncture it, but you can clamp the shit out of it.

edit2: the other thing I would recommend down the line once it's rigged up, would be to get your hands on some "injection molded" trays (as opposed to the flimsier, "blow molded" trays). you wash and reuse them and they would make life easier with that existing shelving in there by not drooping or breaking/falling through. I like to think I'm a gentle, deliberate person, but early morning watering can get clumsy).