As long as the air compressor can keep up with the demand you can hook up as many as you want. That being said, depending on the volume of air needed for each prop, you will hit a limit at some point. The larger the compressor the more props it will run.
Just use 1/4 for all your props, buy union T for three way, four way, or manifold (more then four). These are all 1/4 hose quick connect.
This setup would run you two props
Attach a male 1/4 threaded quick connect into a female compressor fitting. Plug in compressor
Run 1/4 hose to location of split
Union T to split to two other props
Add a regulator before the prop put two 1/4 hose threaded fitting on each side
If you run multiple solenoids for props then you will have to split again or have a solenoid manifold
There is no need for 3/8 hose to each prop. I run 20 pneumatics no problem. Of course I have about 70 gal of air
I've run 3 simple pneumatic props the last few years that all used a single, 12" dual-action cylinder each. And my compressor is practically running non-stop.
This will of course depend on the traffic you have, but we would hit periods of time where there would be a constant flow of people coming through. We queue them up into small groups, but even at that rate I could hear the compressor out back buzzing away.
I have a single line running from the compressor into a manifold that splits the air lines out to the individual props.
The idea of using reserve tanks may help you get through peak periods, but a small compressor is still going to have to peddle to catch up and replenish those tanks as well. Lately I've been worried about what if my compressor were to die, that's pretty much the end of those props, so I've been thinking of adding some redundancy to cover the need for more air and as a backup.
You probably should run this off a hose. You have two options you can plug the bottom with a 3/8 plug this would give you two outputs after. I would just coupler the 3/8 down to 1/4(pipe fitting) and attach a male quick connect on the bottom...this ill give you three outputs.