Have Shed/Man Cave & Need Unground Power Advice
Sounds like cheap is a motivation, but there's a relationship between depth of dig and cost of materials.  


At 24" of cover you can use plain cable such as UF.  
At 18" of cover you can use cheapie PVC conduit or EMT. 
At 6" of cover you can use Rigid metal conduit. 


So as expensive as Rigid might be, it might be significantly cheaper than renting a trencher if you can hand-dig or hydro-dig with a hose to 6".

If you run conduit, you can use THWN-2 single wires instead of expensive, balky cable, and you can go cheap now and add more or larger wires later.   If you use metal conduit, you don't need a ground wire. 

Also if you are cheap, the first thing to shortcut is the 3% voltage drop thing - that was always an old wives tale, is usually computed wrong anyway, and is simply not needed. Also, 100' distances are within 3% even at statutory max current!  


For 20A, use 12 AWG UF or THWN in 1/2" conduit. 
For 30A, 10 AWG " " " 1/2" conduit. 
For 40A, 8 AWG " " " 3/4" conduit 
For 60A, 6 AWG copper ... ... 3/4" conduit or 4 AWG Aluminum in 1" conduit.