I just got a 12 x 18 foot utility shed, 120' from main 200 amp panel. What size subpanel should I use?
Fat conduit, fat aluminum, and fat panels are your friends

Given your circumstances, there is no reason not to provision ample space for future use; some would simply direct bury a 12/3 UF for now, but that means you'll have to dig it up if you want more juice at the shed.  Instead, I would provision a 1.5" and a 1" PVC, buried side by side with 18" of topcover (so about 20"-21" deep); the former provides enough room for a full-sized, 125A, four-wire feeder to the garage, while the latter will be left empty for future use as a communications duct (in case you want to extend network connectivity to the shed, for instance).

Furthermore, unless your AHJ has a severe aluminum allergy, there is no reason not to run fat aluminum for the feeder here.  1/0 Al XHHW-2 is suitable for the hots and neutral on said 125A feeder paired with a 6AWG bare copper ground; of course, if you wish to run a smaller feeder for now, nothing stops you.  Just make sure to run a four-wire feed (two hots, a neutral, and a ground) to the shed!

As to that panel? There's no reason not to get something big and beefy here, either; shop spaces consume panel spaces like a teenager addicted to Mountain Dew, especially if you're doing more than just light woodworking, due to the heavier electrical requirements of machine tools, welders, and other such heavy-duty tooling.  As a result, I'd put in a 24-space or 30-space, 125A, main breaker panel; the main breaker here simply serves as a disconnect, so it's no big deal if it's bigger than the feeder wires going to it.

Since this is a detached structure, you'll need to fit it with a grounding electrode system, too; running more 6AWG copper from the panel to a pair of 8' ground rods spaced 8' apart will get the job done.  Don't forget to make sure your panel has separate neutral and ground bars, with the neutrals all landed on the neutral bar, the grounding wires and grounding electrode conductor all landed on the ground bar, and the neutral isolated from the box!

Last but not least, don't forget to torque all panel and breaker lugs to their labeled torques with a torque screwdriver or inch-pound torque wrench, lest your shed's electrical system give you the loose lugnut!