It's also going to depend on whether you want to handle the snake. Garter snakes aren't the most tractable. Most of the snakes that live off invertebrates are not the easiest to keep in captivity, nor are they good vivarium animals because they'll spend almost all of their time in hiding. If you are a first time snake owner, I don't think I'd recommend any of them for you.
Green snakes, like many insectivores, are pretty shy animals. They don't reproduce readily in captivity so most of the ones in the pet trade are wild caught. It's very important that they have enough plants to hide in and feel secure. You can't just give them a hide box like most snakes. They are partially arboreal so you need fairly large live plants for them to climb on and hide in. If you don't meet all of their specifications, they can be very reluctant to feed. They are considered moderately difficult snake to keep, if you want to do well by them. Not a snake most would consider for a beginner.
The snakes most commonly recommended for beginners are small, easy keepers like some of the corn/rat/king snakes, just like Mulder suggested. However, if you don't want to feed rodents, that rules them out. My feeling is that you'll either have to compromise on what you want to feed, or how difficult the animal is to maintain.
Have you thought about a nice spider? Some of the larger species of tarantulas make great vivarium animals. JMO. They feed mostly on invertebrates and as long as you keep temperature and humidity within certain parameters, there is relatively little to do as far as maintenance. I feed mine less and less often as they mature. My adult female C. crawshayi only eats every month or two, and given her size and weight, I'd bet she could go as long a year without eating, as long as she was not stressed or disturbed. Not usually a problem as handling is pretty much out of the question with this particular species.
Bob