There are only 3 criteria when it comes to air cylinders.
Stroke length: This one is obvious. Pick the one that provides the travel required.
Single or Dual-acting: Single acting has a spring return so they only have one pressure input (usually for extension, ones that retract only are really rare). Dual-acting requires pressure to actuate both directions of travel, so you get full load application for both. You also have to exhaust the side opposite the direction of travel, so the valve you need for them is typically a 5-port directional.
Bore size: This determines the applied load at the rated pressure. A larger bore offers more surface area for the pressure to act upon. This presents a considerable problem for us because nerf is operating at very low pressures and if you use a bore size too small with a pressure too low the applied load on the bore face of the cylinder isn't going to be enough to overcome the friction of the seal on the cylinder itself.
For any air cylinder if you want to determine the load applied at a given pressure you need the following formula
Pressure times Pi times the radius (bore diameter divided by 2) squared: Load = psi(pr2)
If you find that your selected air cylinder will not operate at the pressure you intend to fire darts at you have three courses to take to correct that issue.
1.) Go up in bore size. The bore seal friction doesn't scale at the same rate as the area exposed. Doing a practical test with the cylinder you have of using a scale to see how much force it take to get the cylinder to move by hand will tell you how much load is required to move it. From that you can calculate the minimum operating pressure. This is not a particularly advisable course given you you'll be ordering and returning a bunch of them. The air cylinders you're likely to use are non-serviceable models so replacing the o-ring inside them isn't possible.
2.) Have a different pneumatic control circuit for the air cylinder at a higher pressure rating. This secondary circuit will need its own directional control valve.
3.) Make your own air cylinder. Obvious, but difficult. It allows you to tailor the bore seal for lower friction and select a bore size that will operate at the required pressure level.
All three paths involve wasting a certain amount of your gas supply for actuation. I kind of gave up on the concept of an actuated breech because the secondary issue you have to solve here is efficiency. A flow-control valve on the air cylinder is needed when you are operating one at higher pressures so that the retraction stroke is delayed long enough for the dart to have been fired from the barrel. At lower pressure you would kind of want to use the air in the air cylinder to help fire the dart, but in order to do that you would need some disconnect or catch on the air cylinder itself so that the retract of it is done AFTER the trigger pull, but the side effect would be a puff of air being dispensed by the cylinder stroke. I kind of dumped the ARR project upon the realization that it would an awkward marriage of a springer and an air-powered blaster.
Apparently there's a host of ABSOLUTELY TERRIBLE advice concerning what lubricants can be used with Nerf blasters. Making the wrong choice is likely to result in permanent damage, and even the eventual destruction of your prized plastic possession. DO NOT USE THE SPRAY CANS OF ANY KIND. Any Spray can adhesives are likely to contain petroleum products and solvents in the propellants and those will aggressively damage plastics. Some may even contain alcohol as a thinner.
Ones you should use
1. Silicone - Available in many varieties and applications, and you must select the type that is intended for your use. Certain mixes contain purposed additives or viscosity ratings that could actually hinder performance or potentially damage your Nerf blaster internals.
Get the Silicone GREASE that's available in small tubs. In hardware stores it is usually located near the PVC Solvent Cements.
2. Barium - Harder to find, mostly available from industrial supply. I don't have any personal experience using it myself, but it is used for high-wear applications and in pneumatic control equipment like air cylinders.
3. Dry Teflon pastes - Somewhat expensive but very effective.
Use with caution
1. Lithium - Typically used for bearings this comes as a grease/paste in a variety of specific application options. However any multipurpose lithium grease will work fine so long as it's not one of the varieties with a much thicker blend or too many additives for secondary purposes. The base oil for most "Lithium" Grease is actually mineral oil but the concentration of it is low and the solvent potency of it is low as well. So this one is iffy and depends heavily on which product you purchase because they come in so much variety. The plainer the better.
2. Petroleum Jelly - Pure Petroleum Jelly is compatible with plastics and synthetic rubber, but not advisable for natural rubbers. Avoid any relevant products that include additives for moisturizing (such as chapstick) and be sure that the parts it will be interacting with are chemically compatible.
3. Graphite powder/paste/spray - While it is plastic safe, it is not intended for this type of application. Intended use is for machinery. Also extremely messy. It can work, but isn't advised.
Ones you should not be using under any circumstances.
1. WD-40 - This stuff was NOT DEVELOPED as a lubricant. It primarily is used for water-displacement (where the WD acronym comes from), de-greasing, and rust removal. It will UTTERLY DESTROY O-rings in a fairly short period of time, and will eventually destroy plastics.
2. Vegetable Oil - This is a food product and will eventually start to decompose. You will end up with a bacteria farm inside of your Nerf gun.
3. Mineral Oil - Will penetrate o-rings and cause them to soften and swell. Does the same to any natural or synthetic rubber products.
4. Glycerin based (KY jelly or otherwise) - Also a food product (a sugar) which dries up very quickly and will eventually farm bacteria and make sticky surfaces.
5. "Moly" Grease - These are Mineral Oil based greases. Compatible with plastics, but not compatible with rubber of any type. Their intended application is in ball-bearings.
THE BOTTOM LINE: Just use silicone. Nothing else is intended for this type of application.