That's a very hard question
You can have a minimal system with just reaper and a window manager, or KDE/GNOME with the kitchensink installed. You can most likely configure any distro to run reasonably well.
I've never used it myself, but from what I understand from other people
http://www.bandshed.net/avlinux/ is probably the best solution to wet your feet with linux. It already set up for low latency audio and has loads of audio programs and plugins thanks to
http://kxstudio.linuxaudio.org/Repositories
You could install avlinux on an usb stick and boot from that just for testing.
__________________
Reaper for Linux Documentation (WIP). Software: Archlinux/KDE, Fabfilter FX, Komplete 8, Nebula, Schwa/Stillwell, T-racks Max/Amplitube/SVX, etc. Gear: i7-2600k/4700HQ/16GB, RME Multiface/Babyface, Behringer X32, Genelec 8040, etc. :)