I have a CNC router made from MDF. It's essentially a JGRO design (lots of info available via Google) but slightly expanded to give a cutting area of something like 800x400. It uses a torsion box braced structure as a bed. The only way I would use MDF again is if the bed was on a strong metal (steel/aluminium, doesn't matter) base and well-supported. In which case, why bother with the torsion box, and just use MDF as a spoil board directly on the support structure. In fact, exactly what Jazz has suggested. I can't imagine an MDF structure of the size that you are talking about maintaining any kind of accuracy, even if you can get it flat to start with. I started a thread recently about cutter accuracy, as it seemed as if a 3mm cutter I was using was behaving as if it were about 2.3mm in diameter. The answer was that the machine was bending by the equivalent of 0.35mm when it was taking a cut. Heavy cut? Well, if you think that a 3mm cutter with 1.8mm depth of cut in MDF is heavy cutting...
My next machine (I'm working on design ideas at the moment) will be welded steel. If you have access to welding facilities, steel is not that expensive, and in any case it's the bearing rails, ballscrews and nuts, electronics, etc that are the biggest cost in building. It's not worth taking a short cut to save a few quid on a machine that you will want to earn its keep reliably and consistently.
Raspberry Pi? Yes, they're cheap, and great fun to play with. But they are based on a small, cheap, slow mobile phone processor. It's not obvious at first but what you need is a machine that can handle realtime computing - the job of the computer is to send pulses very fast and with accurate timing to the drive electronics, and that's not even the same as a fast processor. My son has just bought a motherboard for £85 including processor and memory that outperforms (in terms of realtime computing) the PC I use which has, in theory, a faster CPU. You could build a PC based on that motherboard for under £200 that would be a pretty good start, whether you put on Windows and run Mach3 or Ubuntu and run LinuxCNC.
As far as finding a starting design on this forum - good luck! Every so often there's a discussion about having some kind of communal design as a reference, but you won't find two people who will even agree on the basic cutting volume for it, let alone material, cutting speeds, etc! However, there are a number of designs being discussed in the "build logs" area and you should take a look at some of the active threads there that might give you some good ideas about where to start.