Hi, avoid using processed woods like chipboard and MDF as they are made using glue and other chemicals. Any untreated timber will do.
I have built my rabbits play houses that they have had a good chew on from normal untreated timber and they have had no problems.
Your rabbit shouldn't get splinters from the wood. To make sure, check that it has a nice smooth finish (rub your hand on it), and if it doesn't give it a good rub down with sandpaper. You can buy ready sanded wood from B&Q (and any other timber yard I imagine) for cheap.
This is the kind of timber I used to make the frame for the house -
http://www.diy.com/diy/jsp/bq/nav.jsp?action=detail&fh_secondid=9275826&fh_reftheme=promo_159030003%2cseeall%2c%2f%2fcatalog01%2fen_GB%2fcategories%3C{9372016}%2fcategories%3C{9372053}%2fcategories%3C{9372279}&fh_view_size=10&fh_location=%2f%2fcatalog01%2fen_GB%2fcategories%3C{9372016}%2fcategories%3C{9372053}%2fcategories%3C{9372279}%2fcategories%3C{9392120}&fh_eds=%C3%9F&fh_refview=lister&ts=1245427164573&isSearch=false
Neil