Hi, pursing your Jr L1 is a nice step to extend your rocketry knowledge to the next level.
I would recommend scratch build, especially since you have a lot of experience designing and building TARC rockets. You can do it for $30-70 per rocket, depending on how many TARC parts you can re-purpose. Also, if you buy tubes, etc in bulk, you can drive the price down. Using 3d printer and/or laser cutter to create parts will also help to keep your cost down. The NC tends to be pricey, but you can 3d print that.
An H motor (CTI reloadable) runs about $20ish. Yes, club members can obtain them for you and also provide the motor casing to borrow, if you don't have them.
If you come to a club meeting on the 1st, 3rd Tue at the Hatch makerspace in Watertown, it is the best opportunity to meet with club members, get connected to a mentor, ask questions, review designs.
I can send you a base design that one of the college teams use for their L1. You can perhaps use that as a starting point. It has instructions, bill of materials, and open rocket sim file.
You guys are engineers. Definitely use open rocket or rock sim to vet your design. Also, go to thrustcurve.org and look up an H motor, say CTI H133 blue streak. Go to the thrust curve graph and look at the avg and peak thrusts in lbs. You will have to build your rocket to withstand these forces in the bulkheads, fins and glue joints. You can still do it with cardboard and wood, but things will need to be a bit sturdier than for TARC rockets. You guys are TARC, so I probably don't have to tell you this. Try to keep the altitude low, say < 1000 ft, but maintain 5:1 weight to thrust ratio.
Hope this helps. Curtis