Also try contacting local companies, if you want regular supplies then, as above, you need to become a good tip site for a local company and they are best contacted directly. Some tips:
Logs are processed into sizes ready to burn once dry, these are not going to be free as that takes work. If you are a going to be a tip site you need to be asking for wood not logs (arb arisings is the term used here).
As above be flexible. Despite what the internet will tell you all wood burns(!) and releases the same amount of energy per unit weight when dry (when using a wood burner). Less dense wood does take more space but generally that is not so much of an issue (also soft wood generally dries quicker, which can be handy). In fact some softwoods are really good wood to burn once you figure out how to best split them (leave the faster burning woods in bigger chunks).