This is getting a bit convoluted, so let me back up and lay out some general info;
C24 is a control surface and needs nothing else to function as a controller(other than an Ethernet connection). It also has 16 mic preamps and monitor controlling features which you can use(or not, your choice).
Pro Tools HD software will work with nearly any audio interface(since version 9). Since you want to mix in surround, the only "must have" is at least 6 outputs(many interfaces from many companies can cover this).
To use an HD IO, OMNI IO or 192 IO, you need a card that will connect their "Digilink" connection to the computer. That means either an HD card(for Pro Tools 10 or older), and HDX card or an HDN card(for 12.5 and later, this also requires a "Digilink" license on your iLok, $299 by itself).
Let's assume for the moment that you have HD software and want to use Avid hardware but are on a fairly tight budget. An HD/Native card can be found used for under $1k US(remember to add the Digilink license if you have 12.5 or newer). A used 192 IO in the "standard" configuration would have you up and running with the proper cables. This version of the 192 has 8 analog IO and 8 digital IO. You can connect C24 preamps 1-8 via analog(DB-25 cable) and the 192 analog OUTPUTS connect back to the C24(another DB25 cable).
To use the other 8 inputs of the 192, you you need a way to convert analog to digital. In this case, I would skip the C24 preamps(9-16) and buy an external preamp(8 channels) with a digital out. This could be around $200(Behringer ADA8200), $900(Midas XL48 or Audient ASP800) or triple that amount with some other brands(very happy with the Midas here
).
I will stop here as I'm sure your brain is full for now
