Hi Stanley,
The choice is entirely up to you. Both materials have plus and minus points.
I built mine from 1/2" Brazilian ply (not recommended by Richard Shepherd, he prefers one good face Birch ply as in the book), and although it was only ?20 a sheet (B & Q Warehouse), I had to cover the outer surfaces with Car Body Filler to waterproof it and to get a really smooth surface for the paint.
The plus side is that you don't need pilot holes if you are screwing into the ply, but a pilot is needed if passing screws through it and into the battens.
MDF is a harder substance (due to it's construction of Glue and Wood fibre), so it's slightly harder to cut out, and needs pilot holes for all screws secured into it, or the surface 'Puckers' into a small mound. This separates the batten and the MDF, so the glue doesn't contact, weakening the joint.
The plus point is that the surface of MDF is smoother, so you only need to seal it (sealer is available at any good timber suppliers, inc B & Q) and give it a light sanding before painting, this eliminates the hassle of Body finishing the way I had to.
Personally, If I was to build another, I would use MDF for the outer panels which require a good finish (body sides, wing tops and fronts, back panel, etc), and Ply for the rest of the construction.
This would, in my opinion, give the best of both worlds.
Don't rush into things, ask more questions if you're not sure, after all, we all want you to produce the best car that you can, and everyone will try to help and guide you with their experiences I'm sure.
I don't want to be big-headed, but you might find my website useful, just click on the 'Globe' icon at the left of this post, and it will take you there. there's a build blog, pictures, and some line drawings of my build.
Keep Busy,
Regards,
Mark.