Advice on running power to a shed
First, a two pole 25A breaker would allow 25A on each 120v leg of your 240v circuit. All you would need is #10, and maximum allowed amperage for #10 is a 30A breaker. Your service is 200A of 240v, or you could think of it as 200A on each 120v half of the 240v service.
Load calcs are complicated, even if your existing load reaches 160A adding a 60A load/panel would not require a total 60A additional panel to the 160A due to various diversity allowances.
#10 copper is only good for 30A, the next size bigger wire is #8, THWN copper is good for 50A (with #10 ground), and would easily fit in 3/4&quot; conduit. The loads you describe wouldn't require bigger than 30A, but I certainly wouldn't bother, things change. Drop a compressor into the plan and everything changes.
The panel in the shed must be rated for at least the rating of the breaker in the main panel feeding the sub-panel. Bigger rated sub-panel is fine, it will only be good for the breaker feeding it. Also almost all loads now require AFCI or GFCI protection, so full sized breakers must be provisioned, so a 12/24 space panel is now just a 12 space panel. Don't get one that small, things change.
Your shed requires a main disconnect, maybe that is what the 60A disconnect you referenced is for, but the easiest way to accomplish that is with a main breaker panel, with the main breaker 50A or above. A 100A 24 space panel is a good option. The panel needs to have a floating neutral, and a cabinet mounted ground bar. You may need to buy the ground bar separately.
Search &quot;table 300.5&quot; for depth requirements. The table shows cover, the minimum fill required above the conduit.
Edit: NEC 110.14 limits termination ampacity to 60°C if not marked, but allows 75° if marked, modern breakers are marked 75°C. Table 310.16 shows THWN-2 as 90°, but limited by 110.14 to the breaker rating of 75°. Table 310.16 #8 copper in the 75°C column shows 50A.