IIRC the Si32 compact has 16 assignable outputs on the back of the console, at line level on XLR, some of which will probably be in use for the main rig and monitors, but if a reasonable number are unused it would be a convenient way to get line level feeds to a recorder.
Have you spoke to the house tech about how best to skin this cat yet?
I am slightly worried by your not knowing how an electric guitar is normally handled on a stage as this is very basic live sound (And the assumption that the DI sockets on guitar and bass amps are even remotely trustworthy is especially funny), and to be adding recording and video on top of what is already clearly going to be an 'interesting learning experience' is going to make things REALLY STRESSED.
Do you at least understand how to ring out a rig to avoid feedback?
I would figure on a team of at least three people to do what you are trying to do:
One video guy who should JUST be looking after video side (Note that band lighting is more often then not a problem for video, you will want the cameras taken to manual aperture (May require a camera operator per camera as well), and a rack operator at the CCU rack is not a bad idea), close liaison with the lighting guy is a must here.
One live sound guy, responsible for the sound out front (and possibly monitors - important and actually more difficult then just putting the one mix for out front together), possibly also a monitor engineer, but that is scale dependent.
One Recording guy to look after the recording side (and the extra mics that may be required over and above whatever the PA needs).
Doing this with one person is a recipe for red faces all round IMHO.
Have you discussed with the band which aspect of the gig gets priority? The Live experience or the video? Lighting is different between the two, and you will be run off your feet.
Personally I suspect that you are grossly underestimating the sound side of the problem, and that you will run out of setup time big style (Even without the 'in at the deep end' learning live sound at the gig aspect).
Do PLEASE tell the venue technician that you do not really know live sound, they can compensate to some extent by doing some things for you, but will usually stay hands off it they assume you know what you are doing.
Have fun, but I think this will be an INTERESTING experience.
Audiophiles use phono leads because they are unbalanced people!