I use 10 gallon aquariums with screen lids, and I think they are the most inexpensive cage and the easiest to clean. I also use some 5.5 gallon aquariums for some of my dwarfs, but this would be too small for a regular Syrian hamster.
I have used plastic cages before, but I have not had much luck with them. I have found that the hamster chews on it all night long and it is very annoying! They also seem to be a little more costly than other types of cages. I don't want to discourage anyone from using one of these cages, I have just realized that from my own personal experience, that this is not my preference.
I have also used wire cages before and they tend to be a little messy because the hamster will throw bedding out. However, wire cages are better for ventilation. If the cage has a removable wire bottom, I would take it out of the cage. I have never used one of these, but I would guess it could be dangerous. Not only is it bad for an animal to walk on the wire bottoms all the time, but I would be afraid of a little foot getting caught. If you cannot remove the wire bottom, the hamster should have somewhere to get off of the wire bottom, like a piece of wood or plastic or a little house.