I build a lot in this game and it's one of my favorite aspects of the game. But I am always out of wood.
Playing on ps4 so no mods for me yet.
Connie Abernathy (Abernathy Farm) and Supervisor Green (Graygarden) sell 50-weight shipments of wood.
Also, clearing out Spectacle Island will net you almost 4000 units.
Plenty of common junk items are good sources: Brooms, clipboards, pencils, cutting boards, and toy cars can add up fast.
I was wondering why you needed so much wood...I'm pretty sure I've never run out of wood before once I clear Sanctuary. Too bad you can't trade sheep for more...
I always run out of wood too. Whenever possible I make a point to buy all the wood, copper and ceramic I come across. I rarely have shortages of other stuff apart from occasionally, steel.