Well, I'm with Pia in that the word "pet" is a pretty loose term when referring to snakes. They have no real interest in humans, and pretty much just tolerate us, but that certainly doesn't mean they are not rewarding to keep in captivity. If you set up a naturalistic vivarium and can watch their behavior, they can be surprisingly interesting.
To answer your questions...
I always recommend corn snakes to first time snake owners. They're hardy, not generally prone to illnesses that are not brought on by improper care, and their care tends to be fairly straightforward - not requiring a lot of specialized humidity or temperature requirements that some other species do (though they have some, but there's no shortage of corn snake care sheets out there, use the Google!). They do not generally stress easily, and typically do not refuse food for any long period of time. They don't get large (relatively speaking). Giving a general aquarium size depends entirely on what you want to do with it, but somewhere between a 20 and 30 gallon tank (with a secure lid) is generally what is recommended for an adult corn snake - more floor space than height, though they can and will climb. Corn snakes are heavily captive bred so you should have no problem finding a quality breeder, and - as a plus - they come in dozens of different colors and patterns, so they really can appeal to those people who want something cool. Cost can vary from as low as 15 dollars to 300+ dollars, depending on color, pattern, blood-line, etc. There are other commonly captive bred species, like milk snakes and king snakes which also make decent pets for first time snake owners. Personally, my first snake was a ball python. They are also easy to care for, but can get significantly larger, eat larger food items, but can be a little more finicky with stress levels and humidity levels.
As to what they eat, ALL snakes are carnivorous, there is no way around this. Most snakes you will find readily available in the pet trade feed on mice and rats, of which you can buy in various sizes, frozen, from dozens of online vendors, like Rodent Pro
. Thaw them out, warm them up a bit with some warm water, and offer to the snake on the end of a set of tongs. Full grown corn snakes generally eat adult mice, though an especially large one might go up to a prey item the size of small rats.