If you're just looking to cover up the wall, a sheet of 1/4" or 1/2" plywood (4x8') would probably work. You can get them at the big box stores for $20 or less.
I'm not sure how much drywall costs where you are, but my big blue store carries a 4x8' sheet of 1/2" drywall for $8. If you've already got a level and a utility knife, you can cut it to size (score with the knife and snap). If not, those are things you should probably own as a homeowner anyway, so now's as good a time as any to get them! If you want to get fancy, you could get a drywall square; my blue store has one for $12. Throw in tape and a tub of premixed compound for $15 or so, and you're out the door for just more than the plywood. If you've got more than one of these areas to do, you'll only need more drywall making it cheaper overall.
If this is the only place you're needing to fix, it looks like a single 4x8' sheet would cover that whole area, with little left over. In that case, the plywood might be slightly cheaper, but if you need a second sheet for another area, the drywall starts to become cheaper.
Of course, you could just put up the drywall without any compound, making it much cheaper than the plywood.