Let me suggest what I have - a leopard gecko.
Unlike an iguana or some other reptiles, leopard geckos stay small. Mine is fully her adult size, and is about 6-7" including her tail. She lives quite happily in a 10-gallon cheap aquarium. Total startup cost was about $130 - for the tank, the heating pad and light (which I don't use unless it's really cold), rock/cave, and critter. Ongoing cost is a couple dollars every few weeks for crickets. They're very inexpensive compared to a cat or dog, and even more inexpensive if you have an old aquarium around that you can use.
They are solitary creatures, so you don't need to worry about them being lonely, however, unlike some reptiles, they are also friendly. I can take mine out and play with her if I like - she enjoys exploring my desk, crawling on me, etc.
Care is quite easy - I feed mine live crickets, but plenty of people use freeze-dried crickets or whatever if the live ones gross you out. As an adult, she's fed every other day (every day when she was small). Tank cleaning is every month, but is just changing the paper towels at the bottom and wiping it out - takes 10 minutes. She is much easier to care for than my fish.
She also is nocturnal, which is nice if you're the sort of gamer who's playing until 3 in the morning - she'll be most active when you are.
Life expectancy is around 10 years, so as with any pet, make sure this is something you want.
Many pet stores have these available - check in or ask an employee, they may get new shipments in sometimes if they don't have any on hand. Be sure to look at them carefully - they should have all their toes and their tails should be the original tail when you buy them. Missing toes/tails can signify that they've been in too-close living quarters and have been fighting, which can mean they haven't been properly cared for and/or may have illnesses.
I strongly recommend looking in a few pet shops before buying an animal of any sort. I bought my leopard gecko in an individually run store that was absolutely great, but I've seen them in chain stores like PetSmart and PetCo. The ones in the PetCo here are in terrible condition, the ones in PetSmart are okay - this may vary from store to store, of course, but my point is that not every store cares for them properly, so you should look at that when buying one - or when buying any pet.
