Possibly the best solution for moving the emails is not as much about a home network as it is about the method you use. I definitely enjoy having a home network because it allows me to share music and files between my computers and it allows me to give internet access to friends when they come over.
That being said, it sounds like you are using Outlook Express for your email and are going to be moving it to Vista's "Windows Mail", which is a repackaging of the same program.
To do this, you will have to export your email in a format that the Windows Mail in your new laptop can read. Luckily you aren't the first person to do this. Try this instructional page.
The trick is that where this walkthrough assumes you will be moving the data in a thumb drive or other transportable device, if you had a home network set up you could save it directly to the shared directory of your new computer. That's the only difference.
After you have followed the instructions, make sure all of your email has imported properly and then delete it from the Windows XP laptop. Also, remember to delete from your thumb drive or other device the file you used to transfer the email over to the new computer.
If you don't already have wireless set up, it is probably the easiest and most friendly way to have a home network. Microsoft has a good starter introduction to it.
But the basics are pretty basic. If you have DSL or Cable internet already and your "router" or modem doesn't already have a wireless router built in (no antennae), then you'll need a wireless router. Even if you don't have any DSL/Cable service you'll want a wireless router. Check out Netgear, 3Com, and Linksys for these.