If i were buying an External hardrive i'd for for something like this
,Not only is it small but also does not need an external power supply so it's less weight to carry around but also you can use it on a laptop when there are no power points around.About the gaming situation,im not too sure,i see 2 problems:
1.You would also need to carry around the game cd's aswell (Unless that is you are going to use a cracked EXE
2.Some games use the registry (And temporary files) to store data (Registration data and so forth) so using the game on another computer might not work.
So,Some games might work,some games may not.There a few things to know when buying an external hardrive.There is the RPM of the Hardrive (Revolutions per minute) the faster the better,some drives have 5400 and some have 7200.Next of course is the amount of data it can hold,as with before,the bigger the better.Apart from those i cant really think of anything else you need to know when buying an external hardrive.Hope this helps!