Wiring inside plastic shed
The provision you're using is a bit of a fool's errand for most detached structures
The provision in the NEC you're relying on (using GFCI protection at the source end of the buried run to allow for a 12&quot; burial depth with UF cable) is a bit of a fool's errand when feeding a detached structure, as it turns out.  Why? As it turns out, it's not terribly uncommon for things to develop ground faults (vs tripping breakers, even), and if something does trip the GFCI, you'd really rather not have it turn the lights out on you, especially if that something is a circular saw with a rapidly spinning blade on its business end that has a bit of momentum to it.
As a result, it's normally better to accept having to bury the cable or conduit deeper in exchange for having the lighting on a non-GFCI branch, with a GFCI receptacle or deadfront inside the shed providing protection to the receptacles there.  If you're willing to live with that limitation for now, though, given that all you're dealing with are lights and the occasional battery charger, there still are a couple of other points you'll need to keep in mind.
You'll need some sort of disconnecting means at the structure
You'll need a disconnect where power comes into the shed.  If you want an outdoor disconnect, the easiest and cheapest way to do that is using a non-fused pullout disconnect of the type used for air conditioner outdoor units; you could also use one of those inside the shed if you don't care about anyone ever finishing the inside, or you could use a 20A key-operated lightswitch such as a Leviton 1221-2WL in an ordinary box for an indoor disconnect instead since you are only dealing with a single branch circuit.
From there, you don't need to worry about damp
Since this shed has a reasonably functional roof on it, you don't need to treat it as a damp location per se, but there is some cause to be concerned about physical abuse given that there are no studs to speak of in such a shed, so it's much easier for boxes to pinch cables.  As a result, using MC or EMT is not an unreasonable decision in your situation. Note that push-fit connectors are available for both wiring methods, so you don't have to worry about setscrews, clamps, compression nuts, or such; however, you will need to use metal boxes unless you want to do all the inter-connector bonding yourself.  If you do go the cable route, by the way, look at MCI-A type cables (MCAP™ or equivalent) -- these combine the advantages of MC and AC cables in that they need neither the ground wire makeup required with traditional MC nor the &quot;redhead&quot; anti-short bushings required with AC cable; some products even manage to eliminate the normal assembly tape from the equation.