Common Lisp implementations usually are called “systems”, and there are a number for the expert to choose from; I recommend SBCL for new users. Read on for more detail.
In general, Lisp systems are designed around a front end to do development with. However, without an IDE, usually the best usability is to use a system with working arrow keys in the terminal. The author has investigated the CCL and SBCL systems using a plugin called Linedit; this should provide a ramp-up experience.
Using emacs as an IDE and SBCL (Steel Bank Common Lisp) is the most popular choice at this point in time for open source development. Other common systems are CCL (Clozure Common Lisp), CLISP, ABCL (Armed Bear Common Lisp) and ECL (Embeddable Common Lisp). Less common systems exist. This author recommends SBCL or CCL for beginners who are comfortable on the command line, but would like to point out that each Lisp system provides value within the general Common Lisp ecosystem.Note that you can get SBCL packaged with Emacs, Slime, Quicklisp and Git with Portacle, a portable and multiplatform Common Lisp development environment.
LispWorks and Allegro Common Lisp are the currently maintained commercial implementations with IDEs. They provide free limited-functionality personal editions. This author has had good experiences with LispWorks Personal Edition; it has limitations on its use, however.
Mobile developers may find mocl a very interesting product in this space; it is a recently (2013) released Common Lisp system designed for interoperation with the base systems.
Tabulation of systems
|SBCL||Native||High speed compiler|
|CCL||Native||High speed compiler, good on OSX and Windows|
|CLISP||Native||High speed compiler, good on OSX and Windows|
|ECL||C||C interop, has iOS port|
|MOCL||Native||Stores CL as a library for mobile devices - iOS & Android|