You would need a demolition permit from the city to demolish the buildings. Not a big deal, but you would need to have someone confirm that there are NO hazardous materials (as in asbestos, mercury switches, petroleum) in the buildings. It is also the law in this state.
If it were me, I would remove the asphalt shingles first and put them in a pile to be recycled. I would also segregate the clean wood for recycling (keep any pressure treated or creosoted wood out) in another pile. The third pile would be stuff that can't be recycled, like the treated woods, insulation, ceiling tiles, stuff like that. The forth pile would be any steel or wire that could also be recycled.
Stuff that can be recycled costs a lot less to get rid of than stuff that can't be recycled and has to go to a landfill for disposal. Best to separate it as you tear it down if saving money is important to you.
The fire department won't burn it anymore. They only do that to train firefighters and they get plenty of training here already. They probably won't let you burn it in the city either as it is likely to create a nuisance to the neighbors.
Depending on how much stuff you have, you could either 1) have someone drop off a roll off can or 2) load it up in a trailer or make a few trips in the truck/trailer and haul it down to the transfer station.
I would do #2 if it were my money.