I also had a plastic tray one with the removable wire top. Get a big one tho as they need lots of room to run around and can get bored. An essential for the cage is something for them to knaw on and also an exercise wheel. They will spend ALOT of time going round on their wheel. Make sure a shallow dish for food is in the cage too and also make sure you have a water bottle hanging on the side for them. Change the water and food daily. A little house for them to nest in is ideal too as it makes them feel safe. Shredded paper is good for nesting material, or if you run out, just use loo roll or kitchen roll torn into strips. Sawdust is best for their floor.
When choosing a hamster, make sure they are bright and alert. Granted, they might be asleep when you go to the pet shop etc but once you have woken them up, see how they are acting. If they are inquisitive, it's a good sign. A hamster that is lethargic and not bothered might indicate that they are either a runt or poorly. Also watch for clean bums, eyes and ears, as previous mentioned.
Russian hamsters can be a bit spiteful so make sure you know which type of hamster you are buying. Russians might not be suitable for younger children who have never had a pet before because it might put them off handling it if they got nipped by the hamster.
Syrian hamsters (or Golden Hamsters) are bigger than Russian hamsters but are more docile and friendlier. They would probably be more suitable for a child as they are sociable and like to be handled.
Once you get the hamster home, handle it as much as possible (within reason, of course!) so that it gets used to being handled and becomes friendly. Do not be surprised if, when you first get the hamster out and handle it, it literally leaps out of your hands. Be prepared for this and sit on the floor with the hamster so as not to cause injury. If/when it does leap out of your hands, immediately scoop it back up (gently of course) and remain calm and speak to it in a nice tone, stroking too if it'll let you. Every hamster i have had has always done the "leap of faith" but i have always picked them straight back up and held them. They then normally have a wee on my hands or whatever, possibly out of fright, possibly out of scent marking - i'm not too sure about that one. After that, they are normally happy to be handled. Just make sure you handle them frequently. If you get this right, they will look forward to being handled and coming out of their cage.
If you are buying the hamster for the children, depending on their age, it might be best if you handle it for a few days at first, so that it gets used to a pair of calm hands handling it and not those of an excitable child, IYSWIM.
Oh and one more thing. Alot of people tend to make kissy noises at their hamsters/gerbils etc. Hamsters have very delicate hearing and dont actually like this sort of sound as it hurts their ears. Try and keep to low-tone noises and if you make the same sort of noise every time you go to get the hamster out, it will get to know that it is being called and will respond to you!
Enjoy your hamster!!
HTH!