Cheap case to me is anything $10 and under. Surprisingly there is a lot available in this range. Diztronic comes to mind.
I picked up one called Power Support Air Jacket at the Apple Store. It's $30 and very thin. I liked them a lot on the 5S. On the 6+ I'm not so sure. They kind of remind me of the Ringke slim. Hard to put on, even harder to take off. Feels like I'm going to break or bend(!) the phone taking it off. And yes you must follow the directions on removing it or you won't get it off!
It's slim though. It creaks a bit because there's no liner internally. If used in dusty environments I'm sure lots of silica (sand) will make its way in between the jacket and phone causing pitting and minor dings. The polycarbonate is very strong and drops probably won't faze it for the most part. But if you're drop prone a Speck/Otter/UAG/Etc. would provide better protection with the expense of bulk. The phone is thin enough however even with one of the more rugged cases on it does not feel like a brick. But it's noticeable.