Note: Derive was purchased by Texas Instruments and killed off soon afterwards. It is probably difficult to find a copy left on store shelves anywhere now.
Derive leaned more in the direction of clicking on items in the menus to do things, although it was possible to type functions in and even do "real programming" with it to a limited degree. It had a reputation for having very very very few bugs.
Mathematica has always had a reputation for being difficult to get along with. It is a huge system and doubling in size ever couple of years.
Matlab started out as a vector and matrix calculation tool and nothing more. Then they added toolboxes to include computer algebra.
Maple is perhaps the oldest and began as a command line tool that then moved into Windows and GUI.
The best and easiest to use is almost always what the people around you are using. That way you can share questions and answers and leverage off what each other are doing.
There is also Maxima, Reduce, Sage, Axiom (in three variations), Fermat, one or more for the Mac and I just can't remember the names at the moment and even more I can't recall. But, unless you want to ignore the benefits of using what others around you are using and figure it all out for yourself, use what most everyone around you is using.