Could you label where the currents are with arrows in your diagram? So basically label where the currents "I1", "I2", "I3", etc.. are actually going. That way anyone can get an idea of the directions (i.e. In/Out) you're thinking about.
I was going to suggest using a node voltage method but it seems like you're on a good track for this problem.
The first thing I would suggest is you convert all of the components into "impedances". At least for me, it would be easier to analyze the circuit that way.
So think back to what the equation for an inductor, capacitor, and resistor is. That way, you can convert everything into the "s" domain (or omega format, whichever one you want to call it). Then, from there, you can start writing out equations/relationships. See if things might even cancel out when solving for Vout/Vin.
We're not allowed to give "direct" answers to problems on here. I'm just trying to give you tips/advice on what steps to take or approaches to use.