If you are interested in learning a LISP, then Racket makes a lot of sense. It is actively being developed and extended and because of its roots in academia extensions tend to be address interesting problems- many arise out of computer science research by professors and grad students.
On the other hand, if you want to learn Scheme by working through SICP, then I would recommend MIT Scheme to avoid impedance. There's not much benefit from using the Racket ecosystem for that. Likewise, if the goal is to work through On LISP then a common Lisp implementation makes sense.
Of course there's no reason not to have all those languages installed..or at least that's what I tell myself.
My last advice is that Racket is an ecosystem. It provides many languages including Algol and Datalog and Scribble and Typed Racket. This makes for a lot of documentation and it is uneven. The guide will be too shallow and the reference will be more boilerplate rather than providing deeper explanation and further examples.
I've been working through SICP, and as far as I can tell Dr. Racket is actually the best way to do that. You just need to use Neil Van Dyke's SICP package for Racket. http://www.neilvandyke.org/racket-sicp/
FYI, brudgers makes good points, but the beauty of Racket is they have subsets and supersets of languages, from an Algol implementation to a specialized language built for studying SICP. Neil van Dyke and some other Racketeers built it. I think it might be in need of a maintainer, but here it is nonetheless.
Also keep in mind there is a different subset language designed by one of the developer/professors for his own book based upon his improvements to the SICP methodology, entitled How to Design Programs, as explained in his paper.
Felleisen's How to Design Programs has an entirety different set of goals than SICP. HtDP teaches programming practices. SICP teaches 'computer science.'
HtDP is a great book, but no substitute for SICP in terms of content.
While I haven't read HtDP, I've read similar things.
I'm in my late 20s going for a second BS (this time in comp sci), and wanted to go through SICP on my own (plus the online lectures). I felt that I needed a bit of a warmup, though, and chose 'Concrete Abstractions' instead of HtDP. I'm satisfied with it so far.
It may seem obvious but HtDP emphasizes designing programs. It's not really trying to teach theories of computer science or abstractions. It's about developing coding habits - in terms of SICP it's all about good wishful thinking.
SICP, and this is not a criticism, is more like a stamp collection of computer science topics. It provides a point of reference when I've read about operating systems, state machines, compilers, data structures, etc. etc.
Between the two, SICP is flat out a better book qua book. On the other hand, working through just a little of HtDP will probably have more impact on the way you write software than working through a little of SICP.
Lastly, while there may be some similarities to other introductory texts, I doubt that there is any computing pedagogy backed by as much research as Felleisen and the PLT group. While SICP and Scheme were intended to facilitate teaching, the Racket ecosystem [and PLT Scheme before it] are continuously developed with pedagogy as a primary driver.
Most pedagogy is driven by "I think this would be a better way to teach programming." The PLT group checks their theories statistically and their theories are tied to educational theories in general. And they've been going down that road for several decades.
It has admittedly been several years, but I distinctly remember MIT Scheme being an utter pain in the ass to get built. I'd recommend Racket for people just getting off the ground for that reason alone.
However, there hasn't been a release since 2011. The primary maintainer (Chris Hanson) is now at Google, and seems to be busy with other things. Previously, he was at MIT and used to write most of his own research projects in Scheme, so it got a lot more maintenance attention.
Last month I built MIT Scheme on my 13 year old Toshiba Satellite (and it was the cheap one in 2001) under Wary Puppy 5.5. No problems. Because of its richer feature set, Guile was another matter and I gave up.
On the other hand, if you want to learn Scheme by working through SICP, then I would recommend MIT Scheme to avoid impedance. There's not much benefit from using the Racket ecosystem for that. Likewise, if the goal is to work through On LISP then a common Lisp implementation makes sense.
Of course there's no reason not to have all those languages installed..or at least that's what I tell myself.
My last advice is that Racket is an ecosystem. It provides many languages including Algol and Datalog and Scribble and Typed Racket. This makes for a lot of documentation and it is uneven. The guide will be too shallow and the reference will be more boilerplate rather than providing deeper explanation and further examples.