In order to make everything else work, you'll need a 30 or 50A 120v camper outlet. Most farmers won't have one unless they themselves had a camper or a previous owner of the farm did.
A qualified electrician will be needed.
I don't know what you're referring to when you say "not quite true". A 15A outlet and a 20A outlet are pretty much identical. Some 20A outlets have a slightly different blade on one side.
Personally, I've never had good luck getting much to run off of a 15A outlet especially because most of the time, those are run in a series and you likely have other items plugged into that circuit as well.
20A outlets often are for heavier use and may just have one. The likelihood of running a single 13.5k BTU air conditioner off of that is greater.
Keep your extension cord asshort and large as possible.
A generator would really be the best if you're planning on prolonged use.
I was referring to the reply about making everything work and needing an electrician. As I said plugging into a STANDARD 120V/15A, receptacle everything should work just fine EXCEPT AC.
NOTHING in the 120V world is wired in SERIES. THAT is just so wrong and mis leading. EVERYTHING is in Parallel (SAME voltage).
A 20A receptacle will not run a 13.5K BTU unit as the In-Rush current is way over 20A and the breaker will trip. You may get lucky and the AC will start once, every so often NOT on a regular basis.
Also buying a generator is not the solution, UNLESS you buy one capable of supplying 2500 - 3000 watts. The reason being In-Rush current at start up.
However what do I know? I only taught electrical for over 40 years.