Screw it! I couldn't help myself:
You need to sit down and think how you will connect everything. There are numerous ways of doing it, and before you can know how many inputs and outputs are needed on each step you won't be able to tell.
Good things about mixing before using the interface: You can use an interface with less ins and outs.
Bad things about mixing before using the interface: When it's mixed (in the analogue realm before coming into the interface) that's it. You have the mix, not the separate tracks.
However, if you keep the tracks separate as long as possible (all the way into the digital realm, recording it as separate tracks, and perhaps playing it back through the interface as separate tracks), you will have full control all the way, at all times. This means that even when playing back what you made earlier, combined with your "live" performance you can adjust each and everything on the fly.
I know I explained the above like an idiot, but I hope you "get it". Feel free to ask me to explain it again in other terms.
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So, how to connect it all?
Well, to save money, you could indeed sum the tracks, then later on buy an interface with more inputs. This way, you will get used to working digitally, save money, and only spend money on a better interface when you know exactly what you want and need.
Output-wise, you seem to want to do three things: Record at home. Go out and play sets. And allow your kids to play. What will be needed to do each thing? What gear will you have to bring along to play gigs – two turntables, computer, keyboard/controller? What will they be plugged into? Two channel analogue interface? From there it's a matter of counting. I know, It sounds ridiculous, but that's what it is. And what's more, there are more than one way of skinning a cat, so you preferences will evolve depending on how you work or would prefer to work.
I think the best way would be to make some schematics, and then see which interface and/or mixer combination would do the job. And with the different mixer/interface combo see how the schematics could be reworked to make it all work.
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24bits vs. 16bits
In all practicality, this means most in two circumstances:
24bit will supersede the noise floor of most any preamp. It mostly matters when recording low level audio (or speech, for that matter), because it will allow you to stay the hell away from -0db – This is where analogue equipment begin to distort, but digital clips. If it hits the ceiling, it simply won't be recorded.
Now, most likely, you already knew that, but in practice it means one must have the levels high, but low enough so that there is no risk that it will ever touch -0db no matter what happens (no, I don't believe in limiters if they can at all be avoided – they kill the dynamics).
With 24bit you get to have the levels a bit lower, yet having plenty of space down to the noisefloor, allowing you to "lift it" (="normalise" it) later (in the chain or in the recording) digitally without having to hear the noisefloor as would often be the case with 16bits.
If you want to hear some differences between 16bit and 24bit, take a listen to this:
http://www.sounddevices.com/notes/recorders/real-world-24-bits/
(I have no affialitation with them, other than I use their 722-recorder and like their products. Anyway, their examples are good).
Listen to the audio with your best (preferably closed) headphones on.
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KHz (not the whole deal as usual):
According to the Nyquist theorem, which the 44.1kHz of CD's are based on, this yields 22.05Khz of frequency range. This is well above what most people can hear.
In practice, however, this theorem is all but useless the moment you don't record at -0db, use effects or even just play around with the levels (volume).
If you're going to do a lot of that stuff, go for higher sample rates. If most are going to mixed down or played back at 44.1khz, you ought to go for 2x44.1khz=88.2, or 4x44.1=176.4KHz.
If the playback won't be for CD's, you can go for 48, 96, or 192kHz.
If it will be for timecoded MOVIES, well, then it depends where you are in the world, who the producers are, what the production is, and so forth. But here, that hardly matters.
The problem with actually using 192kHz is the space it takes, and how much it takes the chips in the interface. I only use 192kHz, if I am going to make a recording of, say, bats, and having to be able to hear it (one can "cheat" the system by playing back a 192kHz file as a 48khz file, and thus make it play at a quarter of the speed, but at the quality of 48khz).
This brings me back to the doubling and quadroupling of the "CD-kHz". It's simply easier to work with sample rates of 44.1, 88,2 and 176,4Khz in such cases if you want to play around.
192kHz is great if you have the proper equipment, but I would really, once again, advice against it. First of all, it will most likely get you _less_ quality than a decent 96kHz recording, and it will take up twice the space. By all means, go buy an interface capable thereof, but resist the temptation to actually use it actively.
Even if you somehow got hold of a sweet deal (someone gave it to you) on a superb $100.000 digital interface/mixer, it will be unnecessary and would still most likely get you better quality if you recorded in 96kHz on that thing.
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With all this said, I can do my work with whatever is available. Hell, in a pinch I'd do my work with an iPod with mic, a cell phone or whatever (if necessary). It's more important to get it done when it has to be done than anything else. It won't be as good quality as I want it to be, but what I'm trying to say is this: Don't sweat the tech specs too much. Get the basics of digital recording down and care about preamps and how to connect the buggers (i.e. the practical stuff which is just about the same as in the analogue realm ) and most importantly: Do it - even if it's not your dream set-up.