I recently bought a new laptop, and gosh it's great. But I'll tell you, it has been a real chore to migrate all my Sims 3 stuff over to the new computer. You don't really realize how much Sims 3 stuff you accumulate over the years until you are faced with having to pack it all up and install it on a new computer!
external hard drive
Time consuming, but hopefully painless if you plan ahead.
The first thing you should do is bundle up your old family. Do you want to move just your playable Sims to the new computer, or do you want to move your entire town?
If you only want to move your Sims, then the easiest thing to do is upload them to the Exchange. Fire up your game on your old computer, go to Edit Town, click on your family, then click on the "Share" button that looks like a strange windmill. Once this is done, open your Launcher, go to the Uploads section, and upload your family to the Exchange.