Fat conduit is your friend here
I would run 1.5" or 2" PVC conduit here, buried so that the top of the conduit is >18" deep in the ground. The requirements you mention (sand bedding/shading, extra burial depth beyond Code, and warning tape) are typically utility requirements for service conduits; out of these, only the warning tape is mentioned in the NEC, and only for service wires (300.5(D)(3)).
As to inspection, a typical requirement would be rough inspection of the trench and conduit job before backfill with the wires pulled in afterwards, but I would check with your local Code authority (same people you'll pull the permit from) for details.
Since this is an office, by the way, I would throw a second conduit into the trench while you have it open. This conduit will be left spare for now, but provides a place for communications lines to go, whether they be copper pairs, coax cables, or optical fibers. In fact, it's necessary if you want to run copper comms wiring to the office, as that can't share a conduit with the feeder; optical fiber can provided there aren't any conductive members in the fiber cable, but getting it in and out of a shared conduit is a bit tricky.
You can go down to 10AWG copper in the conduit here, but you do need 4 wires
For 240V/30A (your prospective load and then some, split evenly across the two legs of the service) and your given distance, 10AWG copper THHN is more than adequate within your conduit. You will need four wires here, namely two hots, a neutral, and a ground wire, as the ground wire to the main panel provides a path back to the utility for current that came from the utility, while the ground electrode at the shed provides a path back to Earth for current that came from the Earth.
Go big or go home!
One major mistake folks make when they go to put a subpanel in is skimping on spaces in the new panel. The cost difference between a barely-large-enough-for-the-job subpanel and an amply sized one is around $100, given that "amply sized" here is a 24- or 30-space, 125A, main breaker panel. Don't worry about the amp rating of the main breaker here, by the way, since all it is doing is acting as a local shutoff switch for power to the shed.
With a small feeder like yours, by the way, it's going to be fairly important to balance the actual loads across the two legs of the feeder in order to avoid creating a situation where one leg is overloaded by way of being asked to do more than its fair share of the work. This is mostly a matter of thinking about what's hooked up/expected to be plugged into the circuits in question and making sure it comes out mostly even in amps/watts across the two legs.
TORQUE ALL LUGS TO SPEC
One last thing that is required by current Code (2017 NEC 110.14(D)) is that the lugs on the breakers and loadcenter you are installing need to be torqued to the values specified on the label with a torque screwdriver or wrench (nominally, one that reads in inch-pounds, as that's what the labeling uses). Even if your local Code authorities have not adopted the 2017 NEC, it's still a good idea anyway, lest your electrical system do what Greg Biffle's infamous lugnuts did!
