We ship mountain bicycles, but no full suspension unless we don't have enough bicycles to fill a box. We find that the cheap full suspension mountain bicycles wear out too fast, adding to the cost to maintain and/or shortening the life span of the bicycle.
+1 on no cheap suspension bikes I volunteer at a local bike coop and avoid these as bikes to build on the cheap also. For cheap/free usable bikes nicer vintage hard frame Mountain bikes are great supension bikes and road bikes just don't seem to work for charity bikes. Great job I love seeing old bikes get a second life rather than going to the dumb or fixie hell.