Given that you can source basic hand tools (which can do almost everything power tools can do) for a low price, this particular cost saving measure doesn't have a great ROI.
At the end of the day, even with cardboard, you'll still have a working videogame setup, as well as some new, transferable skills (even if woodworking isn't one of them).
I guess what I'm saying is, it doesn't have to be about the thing lasting longer than a month, it's about the process, what you learned along the way, getting something completed and the feelings of accomplishment that go with them.
Personally, I'd be pretty honked off to be €250 into a project that breaks down into un-usability in such a short period of time.
Yes there's no requirement to own a circular saw etc.- as well as hand tools the hardware store will accurately cut wood to sizes you specify for a small fee.
Home Depot and, I think, Lowes will cut for free here in the US. But I wouldn't rely on that for any kind of precision sizing. If you need tolerances within, say, 1/4", you're rolling the dice if you rely on a near-minimum wage employee who couldn't care less doing the cutting for you.