Ideally for side-to-side weight: you want to load it so that you have equal weight distribution on both sides and both axles. But, like you pointed out - you're likely to be heavier on one side due to appliances and trailer design. AND- the few CAT Scales that I've been to wouldn't allow you to weigh individual sides anyway.
For front to back weight, you want to load things so that you have approximately 10%-15% of the loaded trailers weight as tongue weight. That may mean loading things front, middle or rear - it really comes down to your stuff. And, you can only really find that out by going to a scale (CAT Scale or quarry or dump or something like that) and getting weighed. If you're going to go that route, we can provide guidance on what weights to get and how to evaluate those numbers.
Since you're likely at the limits of your trucks rated carrying capacity (GVWR), you *do* want as much stuff in the trailer as possible (assuming you don't exceed *it's* cargo carrying capacity- but at 3,000+ pounds.. you'd have to really try!) and as little stuff in the truck, truck bed and on the truck roof as possible.
The benefit to a 3/4-ton truck or even a properly optioned newer F-150 EcoBoost is that they have higher payload capacities. You said your door sticker on the truck showed a cargo capacity of 1324 lbs. A 3/4-ton (or newer & properly optioned F-150) will have payload capacities at or over 2,000 pounds.
Remember, this truck payload capacity has to handle your weight, wife's weight, hitch, anything you add to the truck (topper, rolltop cover, bed liner, etc.) and anything you carry in or on the truck (bikes, firewood, cooler(s), etc.). 1,300 pounds gets eaten up pretty quick. Myself, my wife, my kids, my truck add-ons, my hitch and all setup weigh close to 1,200 pounds alone. That's before my camper's pin weight gets added.