tuxphobia, i'll try and answer at least some of your questions.
"which is the fastest linux audio distro?"
That's a tough one, that depends on how much effort you put in. Ubuntu, Fedora, and Debian are desktop variants that have versions for making music. Be aware with these distros, that you will face a challenge, and posssibly a conflict between the Jack audio server, and the pulseaudio domestic server that is packaged with these distros by default. There is a wealth of angst on the interlink, detailing the challenges of taking this path. You'll need to decide if your music making box is dedicated to just making and recording music, or as a dual use box, where you wish to play games, do the youtube shuffle, etc...
If you're building a dedicated audio box, then:
My weapon of choice is Gentoo, using what's called the pro-audio overlay. Gentoo can be configured and tweaked to a fine degree for music production.
If you still want a debian based distro, that's fairly easy to setup and use (more or less plug and play), then you might be interested in 64Studio version 3.
"What apps?"
There's a big collection, again depending which way you jump. Google for linux audio apps,and you'll get a long list from which to choose.
"sharing maps."
I wish we could, but we setup maps according to personal wishes, and even 2 VSL users will have different maps.
so it's worth thinking about what you want, and where you want it, then building up maps of your own. Perhaps one day the sample lib manufacturers will have the courage to embrace linux as a viable option (and i can assure you it is) and build generic maps for their products, that users on all platforms can use. Given the surge towards dedicated players, i don't think we'll ever see this day.
"can i route audio/midi over lan?"
Yes you can. You'll need to install JACK on all your machines, choose a master, and make the others slaves. See
http://www.jackaudio.org for details. This sound server uses a protocol called Netjack to manage the streaming.
"My beloved Stylus RMX"
No idea. It's a win app that may or mat not run in an emulation app called WINE. Go to the wine website, and check the application state matrix to see if anyone has tried and tested Stylus in the Wine environment, and what result they ended up with.
Alex.