Personally on as small a layout as it looks like you have, I wouldn't bother with a "mill" or "shortline" engine. If you want to model the MILW, just have a MILW switcher/local switch the branch and logging area. Makes the whole backstory waaaaaaaaaaay simpler. If you want to assign and old 2-8-0 or 2-8-2 a s the local/switcher engine to work the mill fine.
As far as fueling facilities, if the "road" engines are diesel I wouldn't worry about fueling or servicing them at the little branch line terminus. A diesel engine has a range of about 500-750 miles in that era and I would doubt that wherever the "road train" is going its more than 250-350 miles from your branch. Plus having to send small amounts of fuel to a remote, minor engine terminal is very expensive. The railroad would avoid fueling engines there unless its an absolute emergency. It would prefer to service engines at a larger facility where the supplies are cheaper (railroads will even plan where they fuel engines based on state sales tax). In the diesel era, especially post 1960's, they would probably use a GP7 as the branch switcher/local engine, and put GP's on the train that pulled the cars from the branch, then once or twice a week, swap out the branch GP with a engine off the through train, and not even bother with servicing anything on the branch.
If you go with having the branch engine belonging to the railroad, then the only thing you need to worry about servicing is just the engine or engines needed to support the branch itself.