As has already been mentioned....I own a home we don't live in but I pay a service to cut the lawn. It is 3/4 acre. They charge me $45 per cut and mow it every other week. I don't know how long I can pay them for what a new mower would cost. If I were to cut it myself I would buy a 36' to 42" lawn tractor, preferably used, and go at it.
We live on 5 1/2 acres which I used to mow myself. 18 years ago I bought a used Kubota 22 horse diesel lawn tractor with a 60" deck. I believe I paid $6,300 for it. I have some hilly terrain I wouldn't try to cut with a zero turn. I now have a general helper I have hired and he cuts for me on my tractor. It takes him about 6 hours to do the 5 1/2 acres.
I can't see spending lots of money on something fancy just to cut 3/4 acre.
Take care, and good luck!
Rick