I recently did this, as in about a month ago, I became interested in learning Lisp. I started with a bunch of things. First I tried to get various working environments going like:

Emacs + Slime + SBCL

Emacs + Quack + PLT Scheme

I also tried DrScheme (which is a great learning environment).

Not knowing what i'd really need I also did some searching and discovered a few books:

http://mitpress.mit.edu/sicp/

http://www.ccs.neu.edu/home/dorai/t-y-scheme/t-y-scheme.html

http://www.gigamonkeys.com/book/

i also purchased the little schemer. I learned various interesting things from these different sources.

1. practical common lisp was essentially useless to me since i'd already been kind of feeling sold on using scheme and had very little interest in common lisp. what it DID teach me was how datastructures in lisp are created under the hood (or how one might go about implementing them). from this perspective it was very nice and helpful when understading, car, cdr and mapcar. although i wish i'd had a nice example of implementing a scheme in C.

2. reading The Little Schemer, has been the single most satisfying read of my entire computing life. so much so that i bought The Seasoned Schemer and The Reasoned Schemer without hesitation at price. this book will teach you to "think lisp" if you can just make it through the first book you will honestly know everything you need to about the lisp mindset and be ready to actually write useful code and no be shocked or surprised by anything. i can't stress enough how useful this book is READ IT.

3. Teach Yourself Scheme in Fixnum days has been a powerful reference for me and I honestly hope that it grows and evolves, it's easy to reference and great for when you start actually hacking on projects. It's just simple and obvious.

4. SICP is a mammoth work and also has a very nice video series. If you're serious about Lisp and even more serious about Scheme and furthermore serious about computing. You must read this. My approach so far has been to read top down (ie. cover to cover) and also use it as a reference. I get sheer joy from reading it, but it's amazing how practical it can be as well.

Personally I've settled on scheme, i dont' really like common lisp i find it irritating and with projects like Chicken: http://www.call-with-current-continuation.org out there I feel really comfortable. I re-wrote my entire blog using nothing but chicken and the web-scheme egg. I recently wrote an irc bot for fun during a huge bot writing session that broke out in a channel i frequent (don't ask we all just started writing bots for some reason).

If you're looking for good platforms the best I can recommend are:

SBCL (hands down nothing really compares so far)

PLT Scheme (aka DrScheme if you like GUI's)

Chicken (the absolute best imho BSD licensed scheme)

Hope this helps everyone. This is such an awesome thread i hope it continues for awhile.