I agree with the line size calculations for 3% voltage drop and going with #6 or larger is a reasonable and conservative solution. If the voltage drop needs to be controlled, and cost is a non-factor, wire size should be pulled from the tables.
In any system, there is going to be a bottle-neck or a weakest link, and in the system described, the (small) generator/ (big) pump will determine the system performance.
A common design flaw is design for the a future that never arrives. It is usually less expensive to have very modest over-design and plan to rework the system if the requirements change. This depends completely on how likely and how expensive an upgrade will be.
If this is a cabin in the woods, which it sounds like, then future load increases are unlikely, and the quality of the power is already poor. Spec'ing large guage wire won't add much except cost.
When your pump kicks on, you're going to have large voltage drops due to motor starting current, and in a backup or temporary power system, (unlike a home or business) flickering lights are a non-issue.
On the other hand, if you think that a utility hookup is in your future, or that the outbuilding may turn into a spare bedroom, then go conservative. If it was my barn, I'd probably use #8 instead of #4, knowing that I could run a battery charger but not a mig welder.
This also sounds like a 110 system, not a 220, so whether you choose #4, #6 or #8, make sure its 3 wire plus ground, not 2 wire plus ground.