I'm not looking for trophy-size LMB or bream, just decently aggressive fish in the 2-3 pound range for LMB and above average BGs and REs.
You can do that in 3/4 acre.
Local soil and experts will have the best input on whether or not to fertilize, but I think you can build the pond, stock it, and see how your natural fertility is, then decide if you want to fertilize.
... free-range chickens ...
Those can be dangerous, if you chew gum.