What to look for when buying an oscilloscope.

I'm a second year CompE looking to purchase an oscilloscope. I do have access to various labs to use one but I'm always interested in purchasing some of the hardware that I will continue to use in classes and other personal projects.

What are the basic things I should look for when buying an oscilloscope? The ones in my school labs are ancient but they do work. I've been looking into some portable ones such as the DSO Nano v2 and I am wondering if this would be useful at all. I'm also considering some USB oscilloscopes, but I don't know any advantages/disadvantages vs a normal oscilloscope.