Forget AbiWord and Gnumetric. They are not as fully matured and feature rich as OpenOffice.org 3.0. You also don't get the FULLY INTEGRATED feeling you tend to get in openoffice. You also don't get OpenOffice Base, Impress, Draw, etc. From what a senior told me, OpenOffice draw is easy to use but needs learning, and is awesome when used in combination with Impress and Writer. Personally, I just flick diagrams off the internet for my presentations
Anyway, your computer should have no difficulty running OpenOffice since its lighter than MS Office 2007 (Its more comparable to MS Office 2003 in resource usage, which has surprisingly gone DOWN after launch of version 3.0 compared to 2.x series).