Model B is 6'11, Model D is a hair shy of 9'. Either model has the potential to be an exceptional instrument. Realize that there is a lot of variability in a Steinway, two model B's sitting side by side can be day and night. Ask yourself: "does this piano speak to me."
Sounds like the case and the key surfaces have seen better days. These are only cosmetic, and fixing them will generally not change the character of the piano's voice. Are the key surfaces ivory? Something to think about - do you want to find ivory to replace them?
Have the entire thing checked out by a qualified technician. The insides are much more important, and this is where a tech's knowledge is of great value. The evaluation will give you more insight as weather to proceed or not. The evaluation may also give you reason to lower the offer, if there are more things found to be in need of attention. Music school pianos get beat up pretty hard. I've seen practice room pianos brand new in September, and turn out to looking and sounding like a pile of firewood the following April.
I've seen a battered Model B go for around $10k CAN. Keep in mind the new MSRP of these is around $82k from an authorized dealer. You might want to search for a tech who has the expertise to rebuild the instrument so you can also factor in that cost.
Play the piano a lot, test it, prod it, poke it, be a tire kicker. An instrument of this caliber is made to take the beating of a concert pianist.