I'm jealous of your Jake. I briefly owned a 72 Crown tandem-axle, Detroit 671/5sp stick, for historic preservation purposes. Sold it to a friend who was in a better position to restore it. I'd love to get one for the Skoolie project but my bus nut friends would kill me if I ever chopped up a Crown to make an RV. They're a page out of history, and I think us bus nuts should preserve as many as possible. On the other hand, they're lots of fun to drive, and I'd rather see one enjoyed in its second life as a nice camper than go to the scrapyard.
As for brakes, I think any bus longer than 6 rows should have air. Air brakes are more powerful, and have the spring-applied failsafe that will stop the bus in most brake failure situations. Medium-duty vehicles (buses, straight trucks) can be ordered with either air or hydraulic. Heavy-duty vehicles (tractor trailers, larger straight trucks, and don't forget trains) always have air - that tells me something.
I had a brake line blow out on a hydraulic school bus - I was able to stop using the other half of the dual system, but it was pretty scary feeling the pedal go to the floor. The parking brake is designed to stop the bus in an emergency, but I've seen those cables snap when applied for normal parking and let go while buses were parked. In normal use, the adjustable handle (twist the knob at the end of the lever to increase or decrease pressure) tends to loosen up, and some brakes may be "applied" with less than enough force. Most parking brakes are mounted on the driveshaft, and any driveshaft or rear axle failure could render the parking brake useless.
If you blow an air line, you can pull the park knob for a full rear brake application. It won't be the smoothest stop, but unless you're on snow or ice it won't lock the wheels. If anything breaks on the system, aside from a failure of the rear brake components, the parking brake will keep the bus from moving until you get enough air in the system.
For the record, school buses are offered in nearly every size with either hydraulic or air brakes. Gas engines usually had hydrovac. Air was an option on gas buses, but rare. Ford buses ordered with hydraulic from the 80s-90s nearly always had the Lucas-Girling system. Some heavy-duty transit-type buses are only available with air, but I've seen models up to 40 ft (84 capacity) with hydraulic. Internationals from the late 90s and early 2000s could be ordered with hydraulic service brakes but an air parking brake - this was driveshaft-mounted but spring-applied and air-released (other manufacturers also offer this system in buses and trucks). Since 05, International has used a power hydraulic brake system (in lieu of the optional air brakes) which includes a spring-applied electric-hydraulic driveshaft parking brake, and gives the pedal more of an air brake type feel.