Lisp programming and Emacs



Dear community, my question is only implicitly related to Maxima, but I am
sure someone could help:

I wrote some Numerical Analysis functions in Maxima, and they perform very
well. However, I guess a Lisp implementation of those functions would be
faster (and I wonder how faster it will be.) So I decided to rewrite the
functions in Lisp (good opportunity to learn Lisp as well.) I am a big fan
of Emacs, which I use extensively for Maxima sessions, gnuplot sessions, and
as an IDE for Fortran 90 or C/C++ programming. As far I can tell, "Slime" is
the Emacs package for Lisp programming. I installed Slime and SBCL (directly
from Debian GNU/Linux repositories) 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. 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?