> tiny house...
The folks above have pretty much covered your options. Ie. RV's, "mobile homes", and custom anythings not sunk in mother earth. Of course there is the small conventional house of some sort. I think, not sure, there may still be people selling "kit" houses where you pay your money and a flat bed arrives with most of the materials cut and stacked with a short (or long) manual - kinda like the old Heathkit DIY radio concept. From what I know, those are not cheap relative to the other options. The final approach might be to buy (one way or another) a large storage shed and build it into a home; that requires a great deal of knowledge of local law, construction, and type of shed that might suit you. Lots of research definitely a serious investment.
Would it be correct to say that you're looking for a cheap and maybe mobile, in that order, place to sleep and cook and attend to hygiene for a year or two? Do you have any other needs or likes the thing should provide? Regular plumbing? A/C? Stove? Is this (potential) habitat something you look forward to willingly spending thousands of hours building, improving, enhancing, etc? If the answer is "no", that's a really serious constraint and maybe you want to put it front/center in your planning.
The cheapest quick/dirty is probably a used RV trailer. An RV motor home is more expensive because it can move itself - a possibly dubious feature considering the problems that come with. If "mobile" is actually important to you, an RV of some kind is really the only way to go. You can build your own RV trailer and call it a tiny house but it will cost a lot more and there is serious risk of a dead end. It's a HUGE job, done "right". If you want to build with your hands, maybe easier to start "on land" and learn construction where you don't have vehicular complications - ie. look at the shed option.
Back to the RV. They can be a good learning experience, especially if you are broke and shop carefully (being broke really helps to shop carefully...). They vary from "gawd-awful" to "ok" and their shiny sterling virtue, assuming you're cautious and cheap, is that you can throw the first two or three away and write it off as educational expense. As long as you avoid parking tickets. At the very least you'll learn how to stop leaks and put a cheap roof on. <g> Best to start your inspection with your nose. Vermin and mold are non-starters unless you really want to tear it apart and sterilize it.
It doesn't sound right to me to buy a certain vehicle because you want to move something that will likely only move once or twice. U-Haul rents pickups and trucks that can tow most RV's easily. If your habitat is going to (get real now) sit on a piece of land the whole of it's life w/you, maybe just get a standard car that serve your needs in comfort and practicality. Cheap pickups are classic nice, but even if you get a plum, they are _not_ cheap to run.