For tires, look on ebay. A number of sellers have pretty decent nylon gumwall tires that go up to 85 psi and they sell them in a set, two tires, two tubes, and two rim strips, for one price. These are not deluxe tires, but they look fine and hold up well.

Sure, put some oil in the BB, it may rejuvenate the 50-year old grease a bit. Don't expect miracles, and don't put in so much that it starts leaking out, which will be messy. That oil port indicates a pretty old bike; early 60s I guess. It's a holdover from an earlier age when cyclists were irrationally concerned about the inefficiency of greased bearings.