There's the option of a tiny home on wheels. Most states have low sqft requirements for permanent structures, like 650 sqft. If you do the work yourself using professionally created plans, it's possible to do it cheaply and in stages. Once the shell of the house is complete, finishing the inside can be done cheaply by buying discount materials whenever they are available. This is stuff like returned paint and carpet or vinyl remnants (perfect for a small house with small rooms). You can even make a list and ask the local Lowes manager to give you a call if stuff is available. Then there's stuff like Craigslist for free or cheap sinks, counters, furniture, etc.

The biggest issue/cost isn't the actual building codes, as those are easy to meet in most places. It's the sanitation requirements. Those old shacks were allowed to have outhouses, or at least septic systems that would no longer pass. Septic systems are a pain to put in and are quite expensive.