I'm not entirely knowledgable on external harddrives, but i have been looking at them lately. I'd recommend getting a nice firewire one. hmm, just googled your model and it looks like it doesn't have firewire D:
If you want the most bang for your buck, i'd recommend looking for those 500gb external harddrives on sale around the internet. Western Digital or Seagate is what they're usually branded as. They're esata capable, which makes it virtually as fast as an internal harddrive (if you choose to hook it up to a desktop computer) This may not be hardy enough if you're going to take it on the road which i'm assuming you might be considering you have a laptop.
I'd take a look on newegg hurr and see what they have. Just about anything should do.
http://www.newegg.com/ProductSort/SubCategory.asp?SubCategory=414
Also to answer another question, which i don't entirely understand. I think what you're asking is if you save shit on it will you be able to access it on the new computer? Yes you can. external harddrives can connect to other computers. They don't crash a whole lot only if you jostle them. Just don't drop them dude