You cannot use GRI 3.0 even though it has C3 species. It has been specifically tailored for natural gas combustion and C2 and C3 species are for that. C2 nad C3 species should be minor species in fuel if you want to use GRI 3.0.
I would recommend using San Diego mechanism (
http://web.eng.ucsd.edu/mae/groups/combustion/mechanism.html). The lastest revision is dated 2014-02. If you are only modeling freely propagating flame (i am guess flame speed stuff), then you will not need to worry about N2 chemistry. In that case you end up with a reasonably small mechanism.
You can also use USC mechanism as recommended by Nick.