OneNote is a component of the MS Office 2007 suite that is used for note management and info sharing. It is not Office itself.
Yes, OO is free. Personally, I prefer MS Office 2007 SBE. I you want a basic version, the Home & Student spec is good value. Search a store such as eBuyer and you will find lots of flavours of MS Office.
Trial versions are the norm with new hardware.