If in doubt, SHRED IT!
Shred documents with ANY personal information, especially a name; address; social security number; date of birth; etc. Any mail or documents with a bar code need to be shredded too.
To help you with your large shredding needs please visit http://www.thebettershredder.com/index.html. Larry and his team can help you out.
Cross Shredders with a separate slot for CDs are preferable. Affordable shredders can be found at any office supply store, most discount stores, and even the large hardware stores. Check www.craigslist.org or www.ebay.com too.