All the Core2Duo processors are 64bit so you should be good to use the 64 bit version.
Using the 64bit version should give you a marginal performance boost and allows you to use more than 4gb or ram (if you were to upgrade it)
Speaking of upgrades, now would be an excellent time to invest in an SSD. You could install Linux on that and keep windows on the old hard drive, should you ever need to switch back.
All the Core2Duo processors are 64bit so you should be good to use the 64 bit version.
Using the 64bit version should give you a marginal performance boost and allows you to use more than 4gb or ram (if you were to upgrade it)
Speaking of upgrades, now would be an excellent time to invest in an SSD. You could install Linux on that and keep windows on the old hard drive, should you ever need to switch back.