I believe your snake is a Gulf Coast Ribbon Snake, Thamnophis proximus orarius. They are a subspecies of the Western Ribbon and are common all along gulf coast areas from SW Mississippi through Texas. Garters look similar but they typically have black borders on the upper labials (lip scales). It might also be another subspecies of Thamnophis proximus. You can do a web search of the latin name and get further information.
Your cage is plenty large enough but I have concerns about the lid. It looks very escapable to me but I only have the one view of it. If there is any possible way that your pet can escape, he will find it. If it has any plastic parts be sure they do not warp under the lamp or anything. You might be better off with a single piece, tight fitting screen lid weighted a bit at the corners. Ribbon Snakes are also notorious for darting out of their cages so be prepared for that. Like your snake my Eastern Ribbon loves to hide.
Ribbon Snakes, unlike the other members of Thamnophis (Garters) do not take worms. They feed chiefly on amphibians but will also take fish and an occasional lizard. They are also known to scavenge. I highly recommend against amphibians because of internal parasites and there is still some risk of this with a fish diet. My Eastern Ribbon eats large frozen/thawed pinkys scented with goldfish. I scent the pink generously and place it at the opening of his hide. It takes awhile but the snake will eat it. Give the snake privacy and you might have to feed in the evening and leave it in over night. It might take a bit of time and patience but it is worth it if you can convert him to feeding on f/t pinks.
I hope this has been helpful and informative.
Randy
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Firehouse Herps