Welcome to the insanity!
I won't rehash what has been said before because I agree with most of what has been said before. What I don't agree with is mostly personal preference and bias. A Ford vs. Chevy vs. Dodge sort of preference and bias which is not helpful to you at this time.
As far as power source is concerned, diesel is about the only fuel that medium and full sized buses have had since the late '80's. Yes there have been a few gasoline, propane, and CNG buses built but for your purposes the alternative fueled buses are just not appropriate for what you want to do. Gas powered buses are underpowered and thirsty. Propane is even more underpowered and has the issues of fuel availability ( it is getting better but is not available at every freeway interchange in the country) and range. CNG is even worse as far as fuel availability is concerned.
Since you are wanting to move a lot of equipment finding a bus with a lift will make schlepping stuff in and out of the bus much easier. You could load all of your stuff into bins or onto carts with wheels and move them on and off of the bus as easily as a wheelchair.
Look for buses with the 12" windows and not the 9" windows. They are easily picked out of a crowd. The 9" window buses have the top of the side windows even with the top of the driver's window and the top of the service door. The 12" window buses have the top of the windows above the top of the driver's window and the top of the service door.
Even if you don't plan on staying anywhere with ambient temps below freezing the insulation that keeps you warm in those locales will also keep you cooler when you are staying somewhere with ambient temps approaching triple digits.
IMHO the ideal bus is built sometime in the late '90's to early '00's as the engines will not be electronically controlled but will have overdrive automatic transmissions.
The issues you have had with diesels in the past are typical of the sorts of problems electronically controlled engines have. The V-8 diesel you had in the Ford is pretty much identical to the ones available in IHC chassis buses and is known as the T444E. If you get the older non-electronic version it is the T444 and is known to go 300K+ miles with nothing more than regular oil and filter changes and the occasional glow plug replacement. Even more reliable is the Cummins 5.9L/6BT which can be found in Dodge trucks. But the most preferred of the reliable engines are the IHC DT360/466/530 and the Cummins 8.3L/6CT. The IHC I-6 and bigger Cummins are preferred because as every hot rodder will tell you "you can't beat cubic inches". The bigger engines will have more HP/torque and will almost always come paired with heavier duty transmissions with lock up torque convertors--the Allison MT640 or MD3000 series transmissions.
Engines you want to avoid are V-type engines as they generally have less HP, use more fuel, and do not pull hills as well as inline engines.
Engines to avoid are any made by Cat, Mercedes-Benz, and Brazilian Fords. They aren't bad engines but parts, pieces, and service for them are always harder to find and more expensive. Almost any truck stop in the country will have a tech who can work on an IHC or Cummins engine. About the only place you will find someone who will work on a Cat engine is a Cat dealer. Even Freightliner dealers don't like to work on M-B engines. And when you have to go to a Ford/New Holland tractor dealer to get parts and pieces for a Brazilian Ford you can imagine what sort of parts and service you will get.
The vast majority of lift equipped buses are not RE (rear engine) buses and very few of the lift equipped buses are 40' long.
As far as brakes are concerned, air brakes are preferred for various reasons. They are preferred by at least me anyway!
Most air brake equipped buses have greater braking surface and all air brake equipped buses have automatic spring brakes that apply if you should lose air pressure and will stop the bus. Those same spring brakes are used as parking brakes and will secure a bus better than any hand brake that is applied to the driveline.
If you plan on driving a lot of miles the preferred bus is the RE bus. With the engine almost 40' away from where you are sitting while driving you will have very little heat or noise from the engine. RE buses also tend to have the bigger HP engines and if they have luggage compartments usually also have highway gearing.
Almost no school buses will have A/C. If they do the systems rarely work when found in a used bus. They usually take up a lot of space and do little to cool the driver's compartment. But there are some out there and the price is usually elevated by quite a bit over a bus without A/C.
This one does not have a lift but it does have the 12" windows: International 1993 AMTRAN
This one has the 12" windows, the big Cummins, and luggage compartments: 1999 Bluebird All American 75 Passenger - B75518-Used1999Blue BirdAll American
This one does not have a lift but it does have high headroom and pass through under the floor luggage compartments: GILLIG 1968 C190-12
This one will have the 12" windows, a lift, the DT466, the OD transmission, and air brakes: Used 2004 IC CE - Kankakee IL Near Nixa MO - Midwest Transit
This one will have the 12" windows, the DT530, the OD transmission, it is most likely geared to travel at highway speeds, and it has luggage compartments: Used 2004 IC RE - Kankakee IL Near Nixa MO - Midwest Transit
This one will have the 12" windows, the big Cummins, and A/C: Used 2000 Thomas Saf-T-Liner School Bus B85529-Used2000ThomasSaf T Liner HDX
This one will have the 12" windows, a lift, a flat floor, intergrated child seats, the small Cummins, and air brakes: Vehicle Image
This one will have the 9" windows, a lift, track seating, the MT643 transmission, and tinted glass: 1997 BLUEBIRD TC-2000 FE - USED BUS
I hope all of this helps.
Good luck and happy trails to you!