I use Reaper to run live sound. I also have a performance rig for guitar that includes looping with Mobius and recording the rest of the band as well as handling the live sound. Might not be as complex as what you need with backing tracks and all that. I'm pro with the live sound and studio. Not so much with the performance thing.
Reaper is definitely the DAW you want to use for this for stability and flexibility. I wouldn't consider anything else but Reaper and OSX for live sound or literally any other audio job at this point. I'm beyond happy with Reaper.
Since the focus of your rig is live sound which means running at low latency, you ideally want a firewire or thunderbolt interface. For both stability and lower latency at the hardware level so you have headroom to load up on plugins. You mentioned no firewire so, go with thunderbolt then. (I'm told the TB to firewire adapters "just work" FWIW.)
I've had very good performance with a combination of MOTU (for the interface and digital routing) and Apogee (for the converters). RME always gets glowing reviews. UA makes a classy unit. Focusrite gets a lot of bad reviews... They and Presonus are the budget models. Probably not a good choice for live sound in front of a live audience.