I'm planning to commute this winter and am looking to get a spare set of rims to mount my Winter Snow Tires on. The other rims will have slicks that I will use on my trainer. I'd like to avoid having to clean the rims and change tires every night I want to use the trainer.

I'm looking for a cheap set of wheels that are disc brake compatible as they will be used on road and trails in snowy Minneapolis, Minnesota.

I'm new to bike parts and their endless amounts of numbers which is why my google searching has lead me astray.
I am riding a Marin Lombard Cyclocross bike and my current rims are Alex TA-20, 32-hole.

Any info or push in the right direction is greatly appreciated. Just not sure what to look for to make sure I get the right size/width/diameter etc. for my bike.

Thanks!