Welcome!
I’ve been playing around with multistaging for almost a year now and I’ve learned much in that time. My recommendations (which you can skip if you wish) are as follows:
My first recommendation is to be absolutely CERTAIN of your stability margin before you fly. You don’t want an unstable multistager to stage and then become stable while pointed in an unsafe direction. If you’re designing your own multistager or modifying an existing design, use the Barrowman method or a computer simulator like OpenRocket to determine your rocket’s Center of Pressure with the measurements of your actual rocket. Then determine the Center of Gravity in liftoff configuration. Balance the rocket with fresh motors, wadding, and chute all packed. While you’re at it, conduct a swing test. Tie the rocket around the balance point to a long cord and swing it in a circle. Make sure you have enough room to avoid hitting people and objects. If the CG is forward of the CP by at least the diameter of the body tube and the rocket swings nose-first, you’re good. Do all of these checks with each stage combination: booster plus sustainer, followed by removing each additional booster (if present) and finally the sustainer only.
You can avoid much of this work by starting with a multistaging kit, especially a small one. Black powder motors stage without electronics and are a great way to get started. The Estes Twin Factor is an excellent first-time two-stager that flies on any 13mm motor you can throw at it. It stays low so there is absolutely no chance of losing it. Try it in both single- and two-stage configurations. If you’re successful with running it through its paces, consider upgrading to a two-stager with an 18mm mount like the Estes Boosted Bertha. The next sizes up are 24mm and 29mm. For these sizes I like the Estes Comanche-3, the Estes SA-2061 Sasha, and the Dynastar AeroDactyl TS. Try one of each if you can. Remember to put a -0 red-label booster motor in the booster and a motor with an appropriate time delay in the sustainer. Limit your total impulse for the first flight so that you can recover more easily, and be very cautious with wind. Don’t be afraid to scrub a launch if conditions aren’t to your liking.
Once you’ve mastered the fundamentals, you’re ready to stage composite motors. Composites don’t stage like black powder motors, you’ll need staging electronics to detect the booster stage burning out and ignite the upper stage. This holds true even if you’re mixing black powder and composites. A number of staging altimeters are available from a handful of manufacturers. They’re generally pretty small and light, but the bigger challenge is getting a compact, lightweight battery that can produce enough current to fire an igniter. Some lithium polymer (“LiPo”) batteries may work. You’ll then have to work out a feasible way to get the wiring to the igniter.
You generally don’t want ignition via radio from the ground at the model rocket scale. It can be hard to determine exactly when the booster is burned out and staging should occur, if the rocket is sufficiently close to vertical, etc. The signal also might be interfered with unexpectedly and ignite the sustainer when it’s not supposed to, which can be extremely hazardous if this happens on the ground. Having the electronics package be self-contained allows automatic, near-instantaneous staging when you want it and a greater degree of protection against unwanted ignition.
For motor selection, generally you’ll need a booster motor with a good amount of thrust to get off the pad safely and a motor that can ignite reliably in the sustainer. Some are better than others for this purpose. As far as AeroTech’s propellants go, Blue Thunder propellant is pretty easy and pretty thrust-y for a given grain configuration. White Lightning propellant can become stubborn when it oxidizes and Blackjack propellant is sometimes considered a bit more on the anemic side. Each have their own places where they’re best.
Whew! That was a lot. Multistaging is fun, and a great challenge. Learn lots and be safe!