....
>
> but somehow those two are not connected, so I cannot, for
> example, mark a region of a Lisp program and execute it in SBCL
> with keystrokes like C-c C-b, as I do with Maxima programs.
>
>
You may perhaps have not installed everything correctly. I use a
different setup, but in your emacs, did
you try $run-lisp to get an SBCL window?
> In fact, the Lisp program edited in Emacs seems completely on its
> own, not connected with SBCL in any way, although Slime is
> supposed to support SBCL. I tried several solutions which I found
> on the Internet, suggesting adding things in .emacs configuration
> file. However, none of those suggestions worked. So my question
> is, which is the "best" Lisp implementation I should use for
> Maxima-oriented Lisp programming, and how can I use it in Emacs?
>
which lisp? it doesn't matter, I suspect. The same lisp that the
Maxima system is using?