While waiting for your new one download a Linux Live CD and give it a test drive on your older notebook. It will be rather slow, since it will be reading from a CD (or DVD) rather than a much faster hard drive.
There are maybe a hundred variants, each trying to focus on providing what needs to be running on day one to serve a particular community of users. But I would recommend Linux Mint for a couple of reasons. One is that it includes some proprietary codecs needed for running certain types of media files, while many others do not. The second is that is different that the various Windows versions, but it works in ways that a mouser, home user is basically familiar with. In my view, the differences are things that make the user more powerful and using it easier.
You'll need to be sure the notebook's BIOS is set to boot from the CD/DVD drive before the hard drive before you can use ythe Live CD/DVD.
I would start with
http://www.linuxmint.com/edition.php?id=52 if you have no DVD, or with
http://www.linuxmint.com/edition.php?id=55 if you do.
If you want something a bit more tricked out with more of the pretty already there, the KDE desktop look and feel might be worth looking at for comparison: CD at
http://www.linuxmint.com/edition.php?id=61 and DVD at
http://www.linuxmint.com/edition.php?id=61 . There are also three more desktop variants, all within the Mint family.
All come with Firefox as a browser and Thunderbird for email and pretty much everything you will need for anything. Installing is simple and fast, assuming you've already copied off everything you want to save that was on the old computer and are ready to wipe that drive clean. A bit more care is needed if you want to leave Windows running there as another option when booting the machine. And more knowledge, just a bit, will help you make wiser choices during the install using the advanced option. But before you worry about any of that, just give a few of these LiveCD/DVD a test drive or three.
My own path was building a new computer, and while trying to decide whether getting that guy in India to OK putting my OEM XP on it was likely to succeed and the 12 hours of upgrading, adding drivers, and reinstalling everything to keep it from being attacked successfully was worse than sending $100 or more to ill Gates, I decided to try Linux.
A period of time when both the older XP machine seemed easier, and a period of time when Linux Mint seemed increasingly easier and actually far better. Maybe 3 months, and then I just pulled the data drive out of the old one, unplugged it and put it in storage.
Fun for some, or maybe just an unwanted bit of hassle. It can be either, but you may want to play a bit. and help is not far away.