Do I need a compact sewing machine?
Are you considering taking classes? If so, get a compact machine. They are light and easily transported from your home to the location of the class. Just like any other hobby or discipline, classes are a great idea for the novice. With the tools you learn in the classes it is much more likely that you will get "hooked" on sewing rather than letting the machine collect dust in the corner. Once you are "hooked" get yourself a regular, full sized machine. At this point you will better know what you want out of one as well.
What about the more experienced person who has a regular sewing machine and wants to take classes to expand his or her skills? A compact machine is also a good idea. You already know that you will use your at-home machine so think of the compact machine as an investment in your education. Since you are not spending $500+ on a compact machine having one for classes should not be out of the question.
Do I need a serger?
A serger is a specialized sewing machine. They are not as multi-purpose as traditional sewing machines so consider the purchase of one carefully.
If you find yourself doing a lot of seams, a serger is something to look at. Sergers allow the user to skip the step of overstitching the raw edges of a seam. This feature greatly reduces the time spent.
It is unlikely that you would want a serger to be the only sewing machine in your home. While it does some functions exceptionally well it is more difficult to use for others.