No matter what approach you take or how much you spend on alternative energy, you'll need some form of backup power. Any solar photovoltaic system means battery storage and a gas/diesel generator, ditto wind. Batteries are big, expensive and a pain to maintain. Geothermal is a good source of heat, IF you have a powered heat-pump to use it. Alternately, you can drill until you hit a hot layer, but drilling ain't cheap.
For only $10K, I'd connect to the grid. I'd do other things, but that amount is tiny compared to the upfront cost of alternative energy systems and long-term costs of power storage.
If your property has a reasonable amount of wood on it and you enjoy (or are will to learn) wacking up logs, it can be a very good way to heat a place in Maine.
Finally, insulation is your best friend off the grid, or anywhere.