By the time you source all the necessary parts for LC box and Pad box, you may as well purchase a ready made unit that just works very very well. Wilson F/X wired and wireless launch control systems.
https://wilsonfx.com/
Edit:
Please excuse my rather pragmatic initial response to your request for advice. However, my response was based on several years of designing and building wired and wireless launch controllers. Our club has been using these controllers for many years. Due to the growth in the club, it got to the point that we needed a more versatile and expandable system.
The initial launch system the club used was a fully wired 8 channel design with an 8 pad control box multicore-cabled to two 4-channel relay-based pad boxes. When we started launching higher powered rockets using up to L motors, we needed to use much longer cables to the far pads. With at least three pad distances to cover, the cabling became a pain. So, we added RF modules to the controller and pad boxes. This system made it so much easier to set up and use.
However, we were still limited to 8 pads! We needed more. 12 -16 channels is what we were going to need. I was contemplating the additional cost of building the extra channels but quickly decided that that was not very practical. Just to give you an idea of what the cost was for our initial 8-channel wired system, if I recall, was about US$500 to build. Then I added the RF modules for an extra US$200. You could do it more cheaply, but the system might not be very robust, secure and reliable.
You are looking at building a wireless system that has at least 4 channels, but you are very likely to need more sooner or later. I can imagine that your group is not sufficiently cashed up to allow you to spend too much in one hit. However, if you were able to purchase a commercial 4-pad system that is easily expandable to, say, an 8-pad system, or more, at a later stage, then you can spread the cost over time.
Obviously, we don't know your group's details and how you operate with regard to launching model rockets. If your group is in a position to become a Tripoli prefecture, you could then take advantage of the annual TRA prefecture improvement program which can provide up to US$500 for the prefecture. However, this might be a step too far if your group is small and you are only launching low power from a local field. The advantage of this way forward is that you then have insurance cover for your launching that you might not already have.
If you have a technically qualified or experienced person in your group, or have access to someone who is, then they could design and build a wired system initially, that could then at a later stage be easily converted to a wireless system, and also have more pads added when finances allow. This is very doable, but you do need to design it carefully, with expandability in mind. This can keep costs down, but as I mentioned earlier, you can end up paying as much as you would for a commercial system that works straight out of the box and is extremely reliable and expandable.
I would be happy to supply the design details of our old 8-pad club system. You could then assess whether your expenditure on components is within your group's budget. Send me a PM if you want the design schematics. I can send the details of the wired and wireless system, including pictures of the complete system. In my opinion, though, you would be better off with an expandable commercial 4-pad system, as I suggested originally.
In fact, here is a link to our old system that I had for sale some time ago
https://www.rocketryforum.com/threads/8-channel-wireless-cabled-launch-control-system.169904/
Good luck and clear skies!