I would opt for a Linux distro too, if you don't have a copy of Windows there is little point in buying one. As to 32 or 64 bit, that CPU is a 64-bit CPU I believe but since you have only 3GB installed RAM there is nothing to be gained by installing a 64-bit OS. I would go for a 32-bit Linux OS....
I used to run Salent on an old Compaq Presario and that worked very well. There are quite a few lightweight distros about and a lot is just personal taste but Salent worked out of the box and was easy to install.
If not, whilst I'd echo the comments above, I would also just say be careful with compatibility - if your school uses Office heavily, for example, you might miss out some compatibility if you switch to Linux and say Libre Office.