sorry  hit the wrong button...anyway  your ways are way off...heres how to play it
im sure youll agree when u play it this way

Chords- C, G7, F, and back to C
G7 in case u dont know is C when u add your 4th finger to b on the 3rd
fret and move 2nd and 3rd finger over one string each
REGULAR TUNING...FINGER PICKING IS EASIER IF U CAN DO IT WELL
  C         |G7       |F         |C
e-----------------------------0--------------|
b-------1----------3------1-----1--------1---|
g---0-----0----0-----0------2----------0---0-|   REPEAT
d-----2----------0------3----------0^2-------|
a-3------------------------------------------|
E------------3-------------------------------|

then..
e------------------------------------------------|
b------------------------------------------------|
g--2-0-------------------------------------------|
d--3-2-0-2---------------------------------------|
a--------3---------------------------------------|
E------------------------------------------------|