I have an unknown and low-quality classical guitar.

When looking for nylon strings (don't need the top quality stuff), what gauge do I look for?

I have no clue if classical guitars have a standard size, or if I should be looking for something specific. So any info about this would be appreciated.
Classical strings aren't qualified by gauge but by tension. Most classical guitars don't have truss rods, so the higher the tension, the more neck bend and the higher the action. Conversely, higher tension will also create better tone. You will have to find your own preference but I suggest starting with medium tension.
Classical guitar strings aren't enumerated by guage number, as posted above. The three main ones are:

Soft, Medium, and Hard (Heavy) tension strings.

The strings will react differently to unique players and instruments, so it's important to go down the middle road before deciding on whether or not you desire to raise or lower the tension; therefore, go ahead and buy the medium tension strings, so that you may be better able to make a judgement as to what best suits you and your guitar.
My God, it's full of stars!