I'm using the usb-6218 bnc with standard RG-58C coax cables and am getting some noise and ringing in the measurements. I know that the recommended setup is for twisted shielded pairs.
My question is, should these individual bnc cables all be twisted, shielded pairs? Obviously the coax cables are individually shielded, but do I need to pair and twist them and then shield the pair? Or should I not be using the bnc cables at all?
You're going to have to be way more specific for any of us to help. You haven't told us if you're using analog or digital channels, inputs or outputs, how you're measuring and quantifying "some noise and ringing". The "noise and ringing" you're seeing may be completely expected or unexpected. We have no way to know. Please provide a thorough description of your setup, your signals, your grounding configuration, screenshots and measurements of any "noise and ringing" you think is problematic, and a wiring diagram.
For terminology's sake, a coax cable by definition cannot be a twisted pair because the signal and return/shield conductors are in a coaxial configuration. I'm not sure what you mean by "the coax cables are individually shielded, but do I need to pair and twist them and then shield the pair?" There would be no benefit to you twisting two coax cables together if that's what you mean, so don't do that.