Hello

I'm new to this forum, but I joined mainly so I could get help and opinions on this situation. Just yesterday I found a baby garter snake sunning himself on my drive way. I was surprised to see him, considering how cold it has gotten out (it actually has lightly flurried already). I was wondering if these little guys are okay to take from the wild.
I have a five year old bearded dragon, and a four 1/2 year old red eared slider, so I know a bit about reptiles and heating, etc. I looked online a bit about the care and feeding on garters. I've since set up a spare tank with brown paper bag as a substrate, a few fake leaves and branches, a big pool for swimming, and a few hiding spots. This is only the second day I've had him, and I've already tried giving him little guppies and an earthworm I found separated into little pieces, but he doesn't seem interested in either.
So my question is, is it alright to take in a wild garter, will he do okay in captivity, am I including everything he would need, and how long should it take for him to get used to things before he would start eating?
Also the garter is only a baby, he's around 7-8 inches.