There are many cages available for hamsters, but there are many factors to consider when choosing a cage for your Syrian hamster. Most importantly, you want to pick a cage that is large enough, safe, and easy to clean. Unfortunately, many cages you will find at the pet store do not meet all these requirements when it comes to Syrian (golden, teddy bear, black bear) hamsters.
Style of Cage
Your main choices will be between a wire cage (usually on a plastic base), a plastic modular cage (the kind with many compartments and tubes), or an aquarium (with a secure mesh lid). Each style of cage has advantages and disadvantages.
Ease of Cleaning
In general, a wire cage with a plastic tray is the easiest to clean; just lift the wire off the bottom, clean out the bedding, and wipe down the wire part as necessary. The more complex the cage, the more difficult it will be to clean, which is very important if you are looking a plastic cage with multiple compartments and tubes. These cages can become a real chore to clean. Aquariums are not terribly difficult to clean but can be heavy and awkward to handle at cleaning time. Let's face it, cleaning cages is not a fun task, so keeping it easy will make owning a hamster more fun.
A wire cage is easily the best option here. The tubes and enclosed compartments of plastic modular cages can pose real problems with ventilation, so air quality and condensation can become problems. Likewise, aquariums can also have inadequate ventilation. Keep in mind that the openness of wire cages gives them great ventilation but means you must keep the cage out of drafts. Plastic cages and aquariums do offer better protection from drafts.\
Syrian hamsters need ample space to run and play, and the actual floor space of the cage is important for this. In general, many cages marketed for hamsters are too small. Aim for a minimum of 24 inches by 12 inches, and at least 12 inches tall. However, to keep your hamster active and happy, try to get a bigger cage -- when it comes to hamster cages, bigger is always better! Note that the tubes, compartments, and built-in wheels of plastic modular cages are too small for many Syrian hamsters.
Cage Security and Safety
The space between the bars on a Syrian hamster's cage should be no more than 1/2 inch apart. Horizontal bars will allow some opportunity to climb. Check the doors on any cage to make sure they are secure, as hamsters can become quite expert at opening doors (metal bolt clips, like those on the end of a dog leash, can be clipped on to "lock" doors for an extra level of security on wire doors). If you choose a cage with multiple levels, make sure there is no place where your hamster could fall a long distance.
Syrian Hamster Cages and Chewing
The drive and ability of hamsters to chew can affect the type of cage they are suited for. Wire cages have many advantages, but some hamsters become almost obsessive about chewing the bars. If providing ample chew toys and boredom busters don't relieve the chewing, switching to a solid sided cage may be the best option. Also, when choosing a plastic cage, make sure there are no exposed edges or ridges of plastic where a hamster can start chewing the cage, or your hamster is likely to escape at some point. Aquariums are generally chew-proof (but make sure the cover is secure).
Hamsters should have wheels, but it is important with Syrian hamsters to make sure the wheel is big enough. As mentioned, the wheels built into plastic cages are sometimes too small for Syrian hamsters. Ideally, wheels should have a solid surface and no cross bars for support, so no limbs or other body parts get caught.
No matter what style of cage you use, make sure you can provide a nice deep layer of bedding for burrowing. This is most important for wire cages -- choose one with a nice deep tray to allows a nice deep layer of bedding, and also to reduce the amount of bedding your hamsters will push or kick out of the cage.