What a beauty! It's great that he/she is doing so well in captivity. You might want to do a fecal and treat him since most wild caught garters have large parasite loads from the foods they eat. If he is doing well and not stressed, which he certainly seems to be, then maybe you don't need to.
If you post photos of his tail I might be able to sex him. I find that garters are a little different than corns. You could also post the photos on thamnophis.com . There are a lot of very experienced garter keepers there.
Dean gave you all the info on the enclosure requirements although I think that they tolerate lower and higher temps better than corns. Your home's temp might be enough for him. He will be much more active than a corn and a branch or something to climb might be a good idea but he certainly doesn't need one.
Congrats - he is a beauty.