Some great responses above. I'll give you my $0.02 worth...
I'd suggest planning a simple three-fin-and-a-nosecone rocket. Complexity and unique design aren't incompatible with reliability and a low budget, but they certainly don't get along well. I'd also recommend planning on using an Aerotech DMS (single-use) motor rather than a reloadable motor system, unless you can hook up with someone who already has cases, and knows how to use them. Some believe that motor building skill is a prerequisite for high-power rocketeers; I applaud their skills, but don't happen to agree with them. You'll pay about $10 more for the DMS than an equivalent reload - but you don't have to buy the cases and go through the learning curve of building them.
Your first choice should be motor size. Level 1 rockets will generally be 29mm and 38mm motors, Level 2 will generally be 38 and 54mm motors. You can buy/make adapters that would let you put a 38mm motor into a rocket built for a 54mm motor, or a 29mm in a 38mm rocket, if you wish, but that's a bit of complication. Choose 38mm and be happy. In general, level 1 motors will generally cost from $25 to $50 apiece, and level 2 anywhere from $65 to $90 (
https://www.buyrocketmotors.com/38-mm/). You really don't want to know how much the N and O and bigger motors that you read about cost.
The materials you've gonna need for a 3FNC:
1 - Nosecone
2 - Body Tube
3 - Motor Centering Rings
4 - Motor Tube (not strictly necessary)
5 - Motor retention
6. Fins
7 - Parachute
8 - Dual-deploy altimeter, Electronics bay, and second parachute (really not necessary, but if I were mentoring you I'd strongly suggest it for any L2 attempt just from an experience POV).
So let's take these one at a time.
1 Nosecone - Build one. The current rocket I'm building has a bright-orange 3D printed nosecone, and after four iterations (to get the fit into the body tube perfect, etc), total cost has been about $2 worth of filament. Find a friend with a 3d Printer (or go to your public library; many have one), download a nosecone generator for one of the free 3D design packages (I like SCad, but then I'm a programmer so it's pretty natural), and print your own. I wouldn't suggest doing so for a minimum-diameter Mach-3 rocket, because aerodynamic heating will likely cause failure and a spectacular RUD at altitude, but I wouldn't recommend doing such a rocket for your cert flights anyway.
2. Body tube - lot of good suggestions upthread. I happen to have a used 6'x4" shipping tube out in the garage that will someday become a rocket named "Postage Due". However, buying one isn't unthinkable - Apogee Rockets has a nice 4" tube set for $15 (
https://www.apogeerockets.com/Build...n-Tubes/4in-Airframe-Tube-Set?cPath=42_43_55&) that enables a break-in-the-middle rocket, which would be easy to upgrade with an EBay and dual deploy later. The 0.05" thick tubing should also stand up to L1 and smaller L2 motors.
3. Motor Centering Rings - These will be difficult to "find", and moderately difficult to fabricate. The cheapest approach is to buy some 1/4" hardwood plywood, print templates from OpenRocket, glue the templates to the plywood, and cut out the centering rings. But cutting circles reasonably precisely requires a certain amount of equipment, skill and time - I don't have the time, but you might. Otherwise, Apogee Rockets will sell you a pair for $9 (
https://www.apogeerockets.com/Build...h_Power_Centering_Rings/Centering_Rings_38-98)
4. Motor Tube - once again, difficult to "find" unless you have a friend into rocketry. Difficult to build. Once again, Apogee will sell them to you, $6 for a pair:
https://www.apogeerockets.com/Building-Supplies/Body-Tubes/29mm-to-54mm-Tubes/38mm-Engine-Mount-Tube.
5. Motor retention - as suggested above, a screw into the rear centering ring with either a washer or a bent metal clip (
https://www.amazon.com/Hillman-Group-121155-Mirror-Holder/dp/B0050GGPIU/) (don't buy this for $6, that's outrageous) will do fine to hold the motor in place. I do recommend going to a launch to see how HPR motors are held in by a band at the rear of the motor, rather than a stop inside the motor tube, to understand how this would work.
6. Fins - Difficult to find. Can be purchased (for example,
https://www.balsamachining.com/tarc_parts.pdf), or can be fairly easily fabricated by printing templates from OpenRocket, gluing them onto a piece of 1/4" hardwood plywood (you could use 1/8" if you used 5-ply), and cutting them out as long as you use a simple design. Let's be generous, and suggest the piece of plywood might cost you $10 at the local hobby store (
https://www.amazon.com/Midwest-Products-Plywood-Sheet-Beige/dp/B004BPO538/).
7. Parachute - You can build one of these yourself if you have access to a sewing machine (there are threads here about using a canopy from an old umbrella, also). These can get expensive; OpenRocket will be your friend in choosing the right size, but expect to spend anywhere from $30 to $100 for one (e.g.
https://www.apogeerockets.com/Build...48in-Printed-Nylon-Parachute?cPath=42_309_79&).
So, if you built your own nose cone and parachute, you could buy the body tube, centering rings, and motor tube for roughly $30. Add plywood for the fins, and you're up to $40. Add $10 for a couple cheap cans of spray paint and you're up to $50, That gives you a 3 foot tall, 4" diameter rocket and $100 to spend on motors.
If you wanted to pursue this project, I'd suggest getting an idea of what you want to build (look at threads here; lots of people asking "what should I build for my Level 1 Certification"), then install OpenRocket on a PC somewhere (preferably somewhere you have permission to do so) and whip up a design - many of the commercial rockets that you'll find in the "level 1 build" threads have OpenRocket files already available that you could start from. Look through a bunch of vendors - Apogee isn't the cheapest, but they're the most professional and comprehensive that I've found - to find prices on various sizes of components (3" body tube is cheaper than 4", for example). Post your progress here along with any questions or problems you have, and you'll get plenty of help (just make sure that everyone recognizes your cost targets). In a week or so, you could probably have a completed design and a full list of parts that either need to get built or bought.
And that's my opinion. Take it for what it's worth, and what you paid for it.