My new dwarf hamster Basil was gifted to me the other day, and she already is constantly chewing on the plastic tubing in her cage. I'd prefer (safety and aesthetically) to get her a glass aquarium instead. Would a 20½ inch by 10½ inch (12 inch tall) glass fish aquarium work for her? I should I get a 20 gallon instead?
For a dwarf hamster in Germany are a minimal cage space of one square meter (1×1 m or ~40x40 inch) recommended. They are more active than Syrian hamsters, so they need more space. In nature they would have much more space than one square meter as their own territory.
This measure is the ground level of the cage/tank. Upper floors are welcome, but do not count into the one square meter.
In general, a tank is interesting for you because your hamster could not chew on the wires. Plastic is, like you have rightfully noticed, not a good material to chew. But you should think about the conditions inside, for example if the litter (saw dust, straw, hay) is very dusty, this dust will stay inside the tank. Good for your room, but not healthy for the hamster. On the other hand, there won't be cold air movement occurring inside the tank and disturbing your hamster.
Regardless of what type of cage you choose, you have to place things in it your hamster could safely chew on. It is one part of their life to work their self through material to discover new ways. (The other part is digging and burrowing, so they need deep litter.) For example every spring: the plants, bushes and all is growing and they have to hold their favorite ways "clean". So wooden houses/bridges/seesaw will be interesting for you new little friend. Also fresh wood, but you have to get information about the kind of tree or bushes to cut it from.
For more information please see this question: Is this cage too small? (Here are some interesting ideas for low price alternatives to a tank or "normal" cage.)