I always prefer a grant deed or warranty deed. A quitclaim only transfers any of your right in or to the property at the time the deed is signed, but a grant or warranty deed actually changes the ownership.
You should also check to see if there are any real estate tax issues (re-valuation triggers) that kick in when you transfer property in Illinois and if there are any supplemental forms that have to be filled with the Trust Transfer deed. (I have seen those valuation forms in SD, CA and AZ so they are out there in abundance.)
If you have a copy of the grant deed to you (that you received when you bought the property) a real estate attorney in Cook Co would probably do the document and accompanying forms for you at a minimal cost. Check with the Cook Co Bar association for a lawyer referral.