I think it depends on what you're planning on doing with the rocket and how often you'll be able to fly L2. If you're going to mostly fly L1 and occasionally fly an L2, then I'd build a rocket with a 38mm motor mount. That will get you up to baby J motors. If you are planning on using this to fly lots of L2 motors, then I'd go with a 54mm motor mount so you can fly everything up to baby L motors. 38mm and smaller 54mm motors tend to have ejection charges for flying without electronics, but larger 54mm motors don't.
If you're going to fly it a lot, then I'd build fiberglass for a more durable rocket. It looks like you're flying with electronics, so I'd build 4" because it's a lot easier to lay out a bigger sled than a smaller one. If you prioritize slightly cheaper flights*, I'd build a 3" cardboard rocket with a 38mm motor mount. If you want to be able to fly without an FAA waiver, then definitely build a 3" cardboard rocket. If you need to go low because of your waiver altitude, you'll need a 4" or larger rocket.
Beyond the motor mount and tube sizes, it's all about choosing a kit/scratch design that floats your boat. Some people like split fins, some people like scale missiles, etc. Build what makes you happy.
I think most cardboard kits will fit in your budget, and a selection of 3" and 4" fiberglass ones will as well. If you're comparing kits, make sure to check if the kit includes parachutes and hardware. Stuff like that can really add up.
* Nobody does this to save money, but your annual motor/flight budget is a factor. If you only launch a once or twice a year and can spend $500/year on motors, large 54mm motors are on the table. If you want to launch lots of times and have a motor budget of $200/year, then you'll want to stick with 38mm and maybe adapt down to 29mm for many flights.