Hooking up two computer systems

I am currently running Windows XP Pro on a Dell Dimension. My new computer will be a Dell XPS 410 with Vista Home Premium. My IT man says he can hook them up together so that I can use files and programs from my old computer on the new one. He said something about a LAN and a cable router. Are LANS difficult to get used to?

Most of my document files are in OpenOffice format as this old computer came with Corelle's Word Perfect which really isn't compatible with much at all.

I do a lot of photos and photo editing and have programs such as Adobe Photoshop, Picassa, Corelle's Paint Shop Pro and Photo Album. Plus loads of photos, half of which are stored on a Lacie external hard drive.

I have absolutely no experience with LAN's. Am I going to be better off just putting everthing on discs ( 37 gbs) and putting it on the new computer that way,? And getting rid of the old computer - which still works? I bought it in 2003.

I am not very computer literate but am able to read directions 2 or 3 times and understand them. I use my computer for internet browsing, email, buying and selling , photos and photo editing and spreadsheets.

Has anyone had experience with this situation?