Well, for starters, since you have ME currently, you might have a small hdd to start with. To identify this, open up
My Computer and you should see your C: drive. Right click on it and point to
properties. It should look something like this:
http://training.brown.edu/handouts/images/9/9b/Maint_diskcleanup.gif
Tell us the Capacity.
If it is really small to start with, I'd suggest that you should just go out and get a bigger hdd to start with because you can/could see some performance increase. However, if it is sufficient, you can look into what are called "External hard drives" which like you say, is removable. Here is a list of examples from newegg.
http://www.newegg.com/ProductSort/SubCategory.asp?SubCategory=414
What you want to look into is the GB, such as it being 100GB, 250GB, etc.. The more the better, other specs should be looked into also, but if it's the route you want to take, it could be discussed later on to help you find the best one.