What size wire for a 100A sub-panel at 275 feet?
I use Southwire's wire size calculator.
At that length aluminum feeder would be much cheaper, selective boxes for; feet, single (phase), aluminum, direct burial/conduit/overhead, minimum conductor size, input 275 (for the length), input 240v for the voltage, max voltage drop leave at 3 (but we will play with this), current at end (since you don’t know guess at 80), input 1 for parallel sets.
This came up for 2/0 with a standard 3%.
Input in 5 in the %  and the wire size drops to 1 awg with a 4.44% voltage drop
In the US the National Electric Code there are suggestions of 3% and 5% for voltage drop but these are only suggestions.
If you actually used 80 amps of 240v then the drop would be 10.6v with 1awg or #1 wire not a problem.
if you are drawing 50 amps 240v on the #1 wire the voltage drop would be only 6.6volts (got that by playing with the amperage and % voltage drop).
Only during really heavy loading of your circuit would #1 aluminum have a voltage drop that was at the max recommended by the NEC and it never exceeds 5% up to 80 amps.
Going to a larger feeder breaker 90 or 100 requires a larger wire size but I doubt you will need that much power.
I would get the 150 amp panel with more circuits you can feed it with anything below 150 as long as the wire size matches the feeder wire requirements.