Would this be for periodic work on such materials, or day to day? Household machines aren't really designed for day to day work on heavy materials. The question comes up a lot with sewing leather. That being said, it doesn't mean they can't handle it. You have to have the proper thread and needle, and I think the power of the motor can be a factor.
I would think you could try a 66, 15, or 201. Personally, I would try a 66 because they're easy to work on, and I could swap out the Singer motor for a more powerful aftermarket motor if it seemed necessary. I would also consider 50s and 60s era Japanese machines, as long as they're all metal. You could try a 15 clone or a basic ZZ machine, and they usually have higher amp motors.
Where I live 66s and 15s are pretty easy to find, 201s less so. And Japanese ZZ or straight stitch machines are available all the time.
The heaviest material I've sewn is denim; I did have a lady by a 66 from me after she test sewed through 6 layers of it, and the machine didn't even blink. I also had another guy buy a 15 clone after he test sewed a heavier vinyl material he worked with.
I'm sure others will have opinions on this.