A tiny house can easily run under $20,000 fully equipped. Some people have been able to build them for under $10,000.
Fix the house with solar panels, maybe a small wind turbine for electricity. tin roof with a rain water collection, you can run is through a 3 stage or 5 stage filter into a small water tank under a couch. Solar or propane hot water heater, propane gas stove. Grab yourself a 5-mile wifi- antenna to pick up wifi from coffee shops nearby. Composting toilet or a standard RV backwater holding tank to take care of the nasty.
A tiny house with this set up can take care of all of your basic utilities and if you are frugal, resourceful and pick up recyclables, you could drive down the cost possibly under $10k.
Check out this video for my favorite tiny house build. https://www.youtube.com/watch?v=VckbqU4kK2I
Edit: You will need a car/truck that can tow it around. But an automobile would definitely come in handy if you still want to commute into the city.