Primer, maybe? Very good acting, crazy but great plot, good cinematography, but filmed on a budget of $7,000 with deliberately lower res cameras.

Also Pi was also a well acted movie but filmed to look kind of low res.

Clerks? Shot in black and white because the convenience store where they were shooting had lighting that gave everything a weird green color.

Primer. Whole thing done by 2 guys, rented camera, like $10k budget. Brilliant movie.

Inland Empire by David Lynch. Might be a bit of a stretch given that Lynch certainly had the means to film it better, but chose to use a Sony handheld cam for aesthetic reasons.

Also Primer, called the most accurate time-travel movie ever made. Whole thing looks like a 15 year old YT video

El Mariachi (1993)

Maybe not quite that bad, but A Boy and His Dog was a brilliant, dark, sci-fi movie with almost no budget.

Lighthouse with Dafoe maybe