What size extension cord gauge would I need for a 12 amp electric mower if the cord is 250 feet long?
A Gas lawnmower with an electric start. Electric ones don't like to cut heavy dense grass. Plug it in at the house, start it, disconnect and go. A quick search found a self-propelled one for about $300. I couldn't really find one much cheaper but I do recommend a self propelled model. Like this one from Briggs and Stratton, a reputable company.


 -Home Depot

If you're not just going to plug a bunch of regular cords into each other, a legitimately constructed cable and an electric mower would near, if not surpass, the cost of one of these more effective machines.