If you use your input to record into something that does live low-latency monitoring, you can use that to record and use its output to stream using soundflower or jack or whatever.
Honestly, if I were doing that, I’d just use Traktor’s recording and streaming. The mixes on my mixcloud page (which should be linked in my sig) were all made either in Ableton Live as rendered studio mixes or recorded using Traktor’s recording off a random output from my mixer (probably the record out, knowing me) into my FS Open. If you’re having serious issues controlling levels, you can probably get a reasonable outboard limiter for less than the cost of a professional DAW. Plus you get to sound like a stud when you describe it to people.
If you go with a DAW, you want to record the audio direct (simple) and between what gets recorded and what the DAW outputs, you probably want a brickwall limiter with just a bit of gain in front of it…control the unintentional peaks but keep the volume up for streaming. Aim for no more than 2-3 dB of gain reduction at the loudest points.
So, in summary
DJ Mixer → Some input → DAW (record the input) → Gain Stage → Limiter → Soundflower → your streaming program.
Or
DJ Mixer → Hardware Limiter → some input → Traktor for recording & Streaming.
The downsides of the second option are that it’s really easy to squash the sound to death and that once you screw up, you recorded the screw up…in a DAW, you can always render the recording with less limiting (or pre-limiter gain). Your stream will still be messed up because it already happened, but the recording won’t.
The simplest DAW that I know will work is Ableton Live (don’t need Suite but Live Lite doesn’t have what you need), but if you’re willing to find a limiter plugin online somewhere (there are free ones available…OS X comes with one, for example) then you could do it with just about any DAW that does live monitoring.
If you’re not monitoring the DAW’s output and just streaming it online, latency isn’t even really a concern…it just has to do it in real time, even if it takes a second or two to process the audio. Reaper looks like it might be a good choice if you want to take the cheap route (it costs $40 unless you make more than $20,000/year from music) or Ardour might work if you want to take the free route…I just haven’t used it.
If I needed to do that today, I’d probably just use Ableton Live because I already have it…or I’d take advantage of the educational pricing while I can get it and use Pro Tools or Logic just because I could.
