Great question — answering as the UphillTech team:
Different types of insulation have different temperature ratings that effect ampacity, but your cheapest option is #2 direct burial Aluminum, your safest highest capacity is the same #2 Al in 1.25" conduit. Options are: UF cable is limited to 60°C rating, you wouldn't need conduit except $20 at each end where you rise above burial depth. Copper 6/3 UF at retail is about $4 foot. Moderate damage risk, moderate price, lowest effort. More damage resistant would be THWN in conduit. 75°C rating is allowed, copper #8 is about $0.50/ft per strand plus $2/ft. for required conduit. So also $4/ft. More work, minimum risk, more effort (or talent). Highest risk is direct burial #2 AWG Aluminum "Dyke...
Full answer by NoSparksPlease: https://diy.stackexchange.com/a/290152 (CC BY-SA 4.0).
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