Youre correct about the bearings not touching the blade, those are incorrectly set up. As far as the thrust bearing and it being set behind the blade, the only reason that bearing is there is to keep the blade from being pushed off the tires during the cut. When the blade is in motion but not making a cut, the crowning on the wheels should keep the blade tracking with no outside force needed.
As far as general advise goes, youve got a bit of a project ahead of you. Id recommend starting with the basics. First, if you can, disconnect the motor from the saw and let it run on its own. Listen for any noises other than just a gentle hum. While the motor is off, look at the belt that goes from the motor to the drive wheel. Its probably rubber, check for any cracks or fatigue in said rubber. Next, check out the wheels. Make sure the rubber tires on the outer rim arent cracked and still have some grip. Give the wheels a spin, listen for any squeaks, creaks, or anything else. Im with the other two guys on this part, with the age of the saw, youre looking at it having unsealed oiled bearings, which at very best need a good oiling. Id recommend replacing them anyway, bearings are cheap, an ER visit after a bearing explodes and sends a blade in your hand arent.
The wheels and motor are the main working components, assuming they all work and check out okay, all that really needs done is cleaning and tuneup. Cleaning is self-explanatory, go through everything and wipe it down, de-rust the table, etc. Tuneup is also pretty easy to do. Personally, id recommend new tires no matter what, a new blade, and checking out the Wood Whisperers guide to setting up a bandsaw.
Looking forward to seeing the restoration, thats a nice piece of kit. Im pretty jealous actually, ive got a thing for old tools