What size wire for a 300' run to a 60A sub-panel?
Subject to revision depending on your actual loads and how tight the budget is (cheap can be expensive later on, though) I would suggest:
3x 1 AWG aluminum (hot, neutral, hot) 1x 4 AWG Aluminum (but 6 AWG is technically acceptable if cutting it to the bone) Ground. That allows for up to a 100A feed - you may find some use for that, but it also allows for reasonable voltage drop at 50A and 300 feet.
Use 1-1/2&quot; schedule 80 PVC conduit - trenches are expensive, conduit is cheap. If there's any odds you might want even more power at some point, consider 2&quot; conduit. If you might yearn for telephone, intercom, or internet or camera coverage, put in an extra conduit for communications lines. If you are careful about placing the conduit and filling the trench you can save a few bucks by using schedule 40 where it's fully buried - if you are not willing to put the effort into being careful about that, schedule 80 all the way may save you agony. You need schedule 80 where it comes out of the ground anyway (unless you are running this overhead on poles - very retro but acceptable - subject to falling tree damage, though.)
If the shack is &quot;yet to be built&quot; put an UFER ground in the slab or footing, and drive a ground rod outside. Otherwise drive at least two ground rods outside, separated at least 8 feet. Use a 100, 125 or 200A panel at the shack (does not matter so long as it's &quot;at least as big&quot; as the feed breaker) and be sure to remove the bond and keep grounds and neutrals separated (grounds bond to the case, neutrals are isolated from the case.) You require both the grounding system at the &quot;shack&quot; and the grounding wire (connected to them) back to the main feed.
Or if you are SURE 60A is all you'll need and you want to go cheap-as-possible:
3x 4 AWG aluminum (hot neutral hot) + 1x 8 AWG aluminum (Ground) - gets about 6% drop but should still work, and will be less drop when not fully loaded.
That only gets your conduit size down to 1-1/4&quot; - using a 10 AWG copper ground would get you down to 1&quot;.

So, the actual loads appear to be:
Vacuum pump needs 20A breaker, runs at 5.5A, 240V - continuous load (runs more than 3 hours) size for 7 amps (wire has to be sized for 20A due to the breaker, breaker presumably has to be that size to start it.)
Lights etc. 120V loads: 7.5A - use a 15A breaker, 14Ga wire, Provision for 9.5 since lights tend to be continuous loads especially in sugar season.
Reverse Osmosis - 120V at 30A.
So your &quot;actual load at 240V&quot; is 50A (minimum breaker size) to support the 20A 240 and the 30A 120, (the 15A 120 you get &quot;for free&quot; by putting it on the opposite leg from the 30A - you could even add a second one) and your &quot;continuous&quot; load is 16.5 between the lights and the vacuum pump, with the the RO bumping up to 35.5 A (again, the lights become &quot;free&quot; in terms of amperage [not power used] but you have the vacuum pump power added to the RO power, whatever that actually is (using the full 30A for now.)
If you go with the cheap option your RO will be dropping 5% or so if it pulls the full 30A - it probably uses a bit less. You could also pick a size between 4 AWG and 1 AWG to suit your price/performance/expansion or no-plans-for-expansion preferences. If your RO can be reconfigured to use 15A @ 240V you might be able to shrink the wire a bit more.