1) Theres no need to spend much. Sure an expensive ramp will be good, but is it really worth the money if theres only going to be you and your mates using it? I'd suggest leaving the great expense to the councils or private investors wanting to build full skateparks.
2) As far a what wood to use goes, plywood is best for covering your ramps, chipboard, however attractive it may be, is generally not a good idea, as it will rot and disintegrate quickly if left outside. The same goes for mdf or any similar compound boards, and if thats not enough to put you off, with mdf you also get th added risk of cancerous dust, so take care.
3) Now on to answering that all important question - where to get the wood from? Honestly, you will need to buy very little if nothing at all. To construct frames, pallettes seem to work brilliantly. If you go to any builders yard, or anything like an industrial site, they will throw them at you for free. To them it's waste and they have to pay for them to be removed usually. Just don't be shy about asking! 99% of the time they will say yes.
As for where to get the plywood from, we went to a merchants yard, but again, any builders yard might do.We went and asked for any offcuts of ply they could give us, and we came away with a sheet literally as big as a car. And how much did it cost us? �0, yes, absolutely nothing. Ive got absolutely no idea what it was an offcut from, a wooden replica of the titanic maybe, but frankly i don't care.
4) Don't be particuarly picky when you ask for offcuts though. Remember the guys giving it to you are doing you a favour, so just take whatever you're offered. Who knows, even iff you can't think of a use for it at the time, it will come in usefull sometime, and its free so you can't really go wrong! When lookin for ply to cover curved ramps like quarters or kickers/deathboxes, anything from 4mm - 8mm will probably be bendy enough, but if its on the thin side it may require two sheets to stop it from cracking. Anything above 8mm may be bendy enough but could require a few people to hold it in place while you screw it in. Yes if its that thick i would definately use screws not nails as it will pull it off the frame unlike thinner boards.
5) To construct the ramp screws are usually a favourable option to nails, as they wont pull the ply away from the frame like screws will, but they arent strictly necessary, the Rural Heroes quarterpipe is only held together with nails and it's working fine. As to what type of nails, obviously wood nails work best, but masonary nails will also do, as long as the shaft is rounded not square, as it will split the wood otherwise.
Happy building!