How to model a circuit in the s-plane?
You are on the right track.

Just remember that the impedance of a capacitor is

$$ Z_C = \dfrac{1}{sC} $$

These problems, are straight forward to setup but then a lot of algebra. Apply KCL at the intermediate node Vx as,

$$ \dfrac{ V_x - V_i}{R_1} + \dfrac{V_x}{1/(sC_1)} + \dfrac{V_x - V_o}{1/(sC_2)} = 0 $$

Do the same at the Vo node.

The solve the two equations as a function of Vi and Vo.

Eventually you will end up with something of the sort,

$$ Vo = H(s) Vi $$

Then divide each side by Vi.