I'd analyze the first chord as a GMajadd9 chord (DAB - with a low G in the bass), the FGC (on beat 4) is merely a suspension of the previous chord, it can also be analyzed as a Fsus2 chord, however I prefer to hear how the chord functions rather then going by just "naming the chord". When you play the first chord DAB with a low G followed by the FGC with a low G, you can clearly hear the suspension created by the 2nd chord.
I'd suggest as you analyze the piece, to include the bass note at the end of each phrase-let with the chord, as it's a 4 voice texture.
There's a lot of music in this 3 line study. Enjoy!
Nick Cutroneo - Classical Guitarist, performer/teacher/suzuki instructor