think of the "audio interface" and "soundcard" as the same thing (because they are! - BOTH are "soundcards")
 
you do NOT need a soundcard AND an audio interface, you only need the "audio interface" which will convert from A/D and D/A with the inputs and outputs you think you will need, and with low latency ASIO drivers.
 
the onboard soundchip on ALL computers is insufficient.  but a soundcard with mic and line inputs and a couple of line outputs plus a digital I/O (USB2 or Firewire...etc). is what you need.

Just to follow up on 57Gregy’s comment, I changed my MC project sample rate to 48,000 Hz (from 44,100 Hz) and did a few test recordings. This time around, there weren’t any issues with the guitar not syncing up during playback. It looks like that was the underlying issue.
 
I still plan on getting an Audio Interface moving forward – however, I wanted to relay what I found out with respect to the sampling rate in case somebody else has the same problem in the future. 

USB interfaces work fine..... just don't buy a USB mic and expect that to work fine, because it generally doesn't.

yes, if you have a mismatch in sampling rate, even a new audio interface will not solve that problem!