I was thinking about picking up the Game of the Year edition of Fallout 3, and I'm hoping somebody can help me with a couple of questions. 
 
Firstly, I finished the game on an original copy when it was first released, will my existing saves work in the GOTY? Secondly, will all the DLC work with a pre- owned copy?
 
Thanks a lot!

Yeah, your saves will work fine with the GOTY edition.
 
It's not just going to install the DLC, it's going to install the entire game and the DLCs with it. It will save it in a different folder ("fallout 3 goty" instead of "fallout 3"), so it won't overwrite your currently-installed Fallout 3. You can just uninstall the Fallout 3 you have now, but first you must move your game saves, or they will be deleted too. You'll find them in 'Documents > My Games > Fallout3'. Move them to the desktop, uninstall Fallout 3, install the GOTY edition, and move them back (leave the name of the folder as "fallout3" - the GOTY edition uses that folder name too).