Yes, get an interface. If all you ever want is to record the two-track mix, then you only need a two-channel USB or FireWire interface. If you want multitrack recording, get an 8-channel FirewWire interface and connect it to the channel insert outputs of the MG10/2. You will need to use special adaptor plugs for this (such as the Hosa DOC106) in order to avoid breaking the signal connection to the master section of the mixer.
You will need a multichannel audio program for your computer. If you are on a very tight budget, Krystal (free) or Reaper (low cost) would do the job.
My advice would be to get the multichannel interface, even if to start with you only use two channels to record the stereo mix.
Oh, and my other bit of advice would be to keep your fingers away from the CAPS key except at the start of sentences.