I try to mostly burn organic stuff, boxes, paper, wood, and avoid too much plastics/rubber. I will burn milk jugs, laundry detergent jugs, ect that take up a lot if trash can space.
I will throw this out there; couple years ago, mom got a new hot tub, and asked me to haul old one to the dump. They said they wouldn't take it. I thought about hauling it to a abandoned dirt road, like everyone else does, but I don't like that. So, took it to may house, and used an old electric chain saw to cut into about 8 pieces, and snuck the into trash. After about 6 weeks of that, I decided to burn the last 2 pieces; not again; that was nasty, and I ended up putting it out after like 5 minutes.
Point being; if they don't give you an easy, legal thing to do with tires; hot tubs; old fiber glass boats; ect; people will do what they have to do. There are so many tires dumped in the old unbuilt subdivisions around here, its crazy. Same with old TVs, mattresses, ect.
Now; I did come home one day and fire pit smoke was Nasty; and son had dumped 6 gallons of used motor oil in there; yelled at him; and told him dump/auto zone take that crap for free, and to not so that again.