Rexes can be tricky. I f you are still heating your 'environment' whatever it may be, you might put the Rex in a plastic bag for a day or two to make sure the
humidity is adequte while you find a good place for it. Whether or not it needs a terr. environment depends entirely on where you want to grow it. I currently grow all my Rexes in pots with constant bottom watering, but they wear little plastic covers to protect them from the heat in the kitchen where they grow on a table with strong, east light, and they have never been larger, healthier, and most 'colored up' with deep red leaves. See Gallery photo where one is growing its head off and in bloom.

I'm not sure how to find the gallery photo. I've been a member here for a while, but not active at all so I don't know all the features.

I am thinking of planting it in a large canning jar for now.

Aha! figured it out. I saw the picture of your rex begonia. Here is the leaf from my Eeyore.

Looks nice and healthy. Those gallon glass jugs make good terrariums too if you have the room for them. Good luck!