While fibreglass/ carbon fibre would be fun they are not the kind of materials you're likely to get to play with very easily in school environment and they are pretty hazardous materials.
You can use fairly bog standard steel if you're not worried about weight. Its a lot more readily available, cheaper and gives you the chance to experiment and make mistakes without running up big bills, and I'd expect the school would have all the equipment you need sitting there. If you want to learn about and develop a frame design, or even demonstrate something about the geometry then maybe you would make two or three frames.
Slotted dropouts will be the easiest bit, just jigsaw them out of flat plate. I would buy head tube and BB as these need to intersect with bought components so they need to be just so. Beyond that so long as the bike fits you, or at least so long as it isn't far too big and the geometry is broadly in the right range (keeping in mind there are only a few degrees difference between the extremes of mountain bike geometry), then all should be good.
You want assurance that the welds/brazes are good, otherwise so long as the headtube and rear axel are in good alignment the rest should just follow, even if it ends up a bit wonky it will all still work.
The time consuming bit will be preparing the ends of the tubes - cutting the ends of the tubes so they meet at the correct angles and follow the profile of the tube they join too. Try tracing the line of the weld around where you seat tube meets your top tube onto a flat piece of paper - quite a wavy line - now look at all the tubes that meet the bottom bracket - they all need to do that.
Somewhere theres a piece of software that you can use to design a frame - put in all the sizes and angles - and from that it prints out paper templates that you can then wrap around the tubes that map out the cuts you need to make. If you're school as the kit and the skills then you can achieve the same result with a pillar drill and a hole saw, so long as you can get the tubes clamped and supported safely at the correct angles.
If thats all a bit too labour intensive you can look at lugged and brazed frames, old school but a perfectly legit way of putting a frame together. In this case you are buying all the lugs where the joints in the frames are and buying tubes that are sized to match. It like putting together a (very elegant) piece of mechano, but the end result and the decisions about geometry will be the same.
Nick in my workshop* put this prototype together with a tube-notcher (you can get a similar result with a pillar drill and a holesaw and some careful clamping) and a tube bender. Admittedly he is an engineer, but he'd never built a bike before and it all worked out first time.
*actually its his workshop, I just take up all the space
