Another issue I think you might encounter is that most doors are hollow or partially hollow to keep the weight low. There is significantly less wood in a door than it would seem. They're usually frames with panels. Some main entrance doors are solid, but they tend to be problematic as they
experience seasonal expansion and contraction with humidity changes.
Pallet wood can be a good free alternative if you can verify how it's treated. Also you can probably get round wood that has been cut down (because of growing towards power lines or other similar problems) for free if you keep an eye out while roaming about your locality.
Other deceptive "wood" sources are cheap furniture left on the roadside - most of it is particle board which is as much glue as wood.
I got a load of round cedar lumber from a friend who thinned his woodland for the equivalent of about 60 US dollars. It was more than
enough to build six raised beds and enough leftover for stakes and other small uses. I think he would have given it to me for free, but he was happy to have the cash.