Depends on how serious you are about graphic editing, what you plan to do with the pictures and how much you want to spend.
If you are an amateur and you just want to make nice pictures for yourself and free, forgo Illustrator all together and get the free program GIMP. It does most of what Illustrator does, and can even use most of the Brushes and other extras for Illustrator, but is free.
If you still want to use one of the Adobe products, go with Elements. It is a stripped down version designed for home usage. It will let you edit pictures and do design for a reasonable price. It includes all the graphic editing tools of Illustrator.
Illustrator also includes tools for doing web page design. If you are not going to be creating web pages, you probably do not need those tools. Most people would never use them. Adobe Elements is enough.
However if you are planning to design web pages, then go with the CS4, CS5 or CS6 versions of Illustrator. But be prepared to pay several hundred dollars for them. CS4 is the earliest version, replaced by CS5. Because it is "last year's" version, you can often get it for a lot less money. CS5 is the most used version. CS6 has just been released (have not seen it yet to know how it differnces from 5, but appears to be minimal)
Hope that helps...