PVC is inexpensive conduit, which can be good, but it requires an expensive trench (whether or not you are in Kentucky) when running power.
More expensive Rigid or IMC steel conduit may let you have a less expensive trench, and also serves as the Grounding (not Grounded) conductor. You need 4 conductors for typical 120/240 USA/Canada service - Two Hots, one Grounded (Neutral), one Equipment Grounding Conductor (which can be the conduit for steel conduit. Otherwise, it's 4 actual wires.)
The minimum cover requirement (general) is 6" for Rigid or IMC, and 18" for NMC (that is, PVC or other non-metallic conduit.) That is from the surface to the closest part of the conduit (not the bottom of the trench, the top of the conduit.)
Depth can be reduced by adding concrete on top. Depth increases (generally) for running under driveways, though for "one or two family dwelling driveways used only for dweling related purposes" it remains at 18" for NMC (but it increases to 18" if using rigid or IMC.)
Using cable (rather than individual conductors) inside conduit is madness, generally speaking, as it's very hard to pull and greatly increases the size of conduit you need for the fill calculations. If you want to "add protection" use only schedule 80, no schedule 40, and carefully backfill with sand or finely screened material around the conduit rather than pushing dirt/rocks back on top of the conduit. Or contemplate concrete cover, and save on the trench depth.
Add a separate communications conduit (possibly empty at present, but so handy if you ever run network wire or fiber) while you have a trench open, and be sure to place "buried electric line below" tape in the top 6" of the trench.
As for wire size, it depends on what you would actually like to allow for - if only 60A service, 3 gauge aluminum would be adequate and far cheaper than copper - 2, 1, or 1/0 would allow more amperage if desired at some point in the future (or now, since it's cheaper in the long run to simply buy a bigger panel once, than to buy a smaller panel and replace it with a bigger panel later.) The amperage draw of your air conditioner may be a deciding factor, and you have not provided that information - if it uses potentially 30 amps and you want a typical "shop service" of 50-60 amps available without having to worry about whether the air conditioner is running, you might want to plan for 100 amps to be safe. If it's only 15 amps, that might not be as much of a concern, or you could go for 75 amps (but it's an odd size - a 100 amp panel may be cheaper, due to volume of sales.)
For the average home electrical worker, I think it's safest to run all the wire, then hire an electrician for a short stint actually making the aluminum connections - the newer alloys are not the scary stuff the old 10/12Ga aluminum was, but it's still a bit of a process connecting them properly, and experience in doing that is worth paying a pro to do, in my opinion. If not, read up carefully on the proper procedure and follow it, including joint goop, stainless steel brushes, and using a torque wrench on the connecting bolts.
2 inch schedule 80 provides plenty of room for 4 1/0 conductors. You can downsize the grounding conductor and possibly get down to an acceptable fill for 1-1/2", but it will be a miserable pull, so I'd stick with 2 inch and a comfortable pull. If going with 2 or 3 AWG, 1-1/4 inch would do, but 1-1/2 inch (or 2 inch) would be easier. Your grounding conductor only needs to be 6 or 8 AWG aluminum for 100 or 60 amp service (i.e. 3x 1/0 and 1x 6AWG is perfectly acceptable for 100 amps.)
