I am a current FTC student so I feel qualified to answer this.
One of the biggest and most important components of FTC is the engineering notebook. Writing a good engineering notebook is the key to success. There is not a single perfect formula for an award-winning notebook, but the biggest thing is to record everything that happens. Write about crazy robot ideas even if they are too hard to build or just not a great idea for the game. Write about successes, failures and everything in between. Take pictures of the process also. Building a prototype? Take a picture for the notebook. Drawing our or CADing? Throw a picture/screenshot into the notebook. My team uses google drive for our notebook and we have a super long document with everything from the season. It is also important that the notebook meets all of the requirements for each award so check FTC Game Manual 1 which comes out in the summer but rarely changes year-year.
The second biggest thing is the robot of course! There are three major ways to go about building the bot (imo).
1: Kit of Parts/build system. There are three major build systems/parts kits that can be used. Textrix, REV, and Actobotics. Each of the three works great, but there are also drawbacks to each. The most important thing about using a build system is to go ALL in and to make sure that you have all elements for that system so that the team is not limited by the basic kit. Also remember that the kit is not the end all be all so there will be wheels and motors and other elements that students probably want to have from other vendors. I don’t have a personal preference about which build system as my team has used way 2 (talked about below) and way 3 (below).
2: Build system tornado (couldn’t think of another word)/extrusion bot. Some basic parts, andymark motors, chain, sprockets, compliant wheels, stealth wheels, 4" omni wheels, servo city motor mounts, and some other basic items can go a long way paired with extrusion. My team has used 8020 extrusion but that is a little much for FTC thought I would guess you have a good amount in the shop since you are a part of a larger FRC team. Extrusion + other parts can be very innovative and a good way to build a creative robot.
3: Custom bot. Paired with CNC access, 3D printers and/or laser cutters, teams can build some pretty neat custom robots. If you have access to these and have members that know how to CAD, an awesome robot can be made. Of course, going this way motors, chain, sprockets, gears and some other things will be needed.
There is no one way to do FTC, but having mentors who can get the team going on a design that will work for FTC and having students who are dedicated in writing the notebook will go a long way.
Also, there are more FTC people on the FTC Reddit and discord, so consider joining those forums to ask more questions! Also, you can email my team directly at firstname.lastname@example.org if you have any specific questions. We just got done competing in our 9th year of FTC and have lots of knowledge about the program as a whole.