I think several people have already pointed out that using straw bales with modern stud building practices may cause more headaches than you want.
If you want cheap, I would normally say that pink fiberglass stuff. You don't want synthetic. I would suggest rockwool (mostly stone and slag, so fairly "natural"), sheep wool insulation, hemp batt insulation, or hempcrete. All of those are natural and would work fine with stud construction... but they are also fairly expensive.
In general, for a house, especially something on the inside of the walls, I would be looking for the best I could afford... not the cheapest, but I get it, especially with prices rising.
Given your restrictions, straw might be the cheapest option, but make sure you include the cost of plaster and maybe compare it to something like rockwool or hemp batt insulation. For a 500sqft house it might not be too bad. You might also be able to build your frame, then just stack the bales of straw around the outside and cover it in plaster. Your roof would have to be a bit wider to cover things, but there is no reason the insulation has to go in between the studs. You might be able to save on the outside cladding of the house if its done right.
Good luck and let us know what you choose and how it goes.
PS this
thread talks about some realities of straw bale houses. Some people like them and others have not had very good luck with them.
https://permies.com/t/113626/Straw-Bale-Don