I've kept and bred leos for a few years now. They are personable if handled but not overhandled and some are pretty, but as animals in the reptile world go they can be disappointing because they're not terribly interesting to watch. They spend most of their time sleeping and hiding. Don't want to discourage you though, I love them!
If you want to keep three of the same sex, you need females because males will fight to the death. You would need a 20 gallon for three, a ten gallon is plenty for one pushing it for two, too small for three. I don't recommend keeping three together right off the bat anyway though if you have no experience with reptiles. Leopard geckos are easy to keep but can be prone to eating problems etc. It's awfully hard to tell if one is sick and not eating until you see really serious symptoms when you're housing them together. All you see is that the food is gone, no idea usually who ate what. So I would say start out with one, get used to the signs of a happy gecko and an unhappy gecko and then expand. Plus the biggest reason to house them together is for breeding purposes, they are not
social animals and don't have any really interesting behaviors when they interact with eachother. For the most part they are happier and less stressed when not housed together.
Some additional info: you'll need an undertank heater (get a real one don't use a heat pad). They eat live insects. It's best to get as much variety as possible. Mine eat crickets and
meal worms with the occasional wax worm or (when they're full grown) pinky mouse if they need to fatten up. Shallow bowl of clean water should be available at all times. Waxies and pinkies are high fat so don't over do it with these items, also if you start out with babies or juveniles, remember not to give them a prey item any longer than the space between their eyes. You can get fancy with substrates, but I do papertowels. This way you can clean easily, they don't ingest substrate when they're hunting bugs, and you can tell easily if there's something weird about their poo + it's cheap. You will need to get a calcium, vitamin D + other vitamin dust. Read the instructions on the back, most say to dust their insects with this mixture once ever 3 feedings for adults or something like that. Remember juveniles or females laying eggs require more. They don't need climbing spaces but do need hides, place one on the warm side of the tank over the heat pad, and one on the cool side. This way they can thermoregulate. They can be prone to shedding problems that can lead to infection or loss of limb. If you notice this increase calcium in the diet, provide a humid hide, and if necessary soak the animal in shallow warm water. Any time a leo stops eating is cause for concern, if this continues for a few days, a vet visit is necessary. Make sure you know a REPUTABLE reptile vet before purchasing the gecko. Remember, leos are better than most reptiles about being handled, but no reptile requires or enjoys handling persay. In spite of their laid back, docile nature, there has been more than one leo who was essentially loved to death (aka died due to stress from overhandling). Two to three times a week for 15 to 20 minutes at a time wont hurt, more than that could. That should do it for the basics. Let me know if you have any questions.