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 spuare meter (1×1m or ~40x40inch) recommended. They are more active than syrian hamsters so they need more space. In nature they would have a much more than one square meter as their own territory.
This measure is the ground 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 right have 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 inside the tank will not be cold wind disturbing your hamster.
Equal what type of cage you choose you have to do 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 has to inform 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 prize alternatives to a tank or "normal" cage)