Configuring Frequency Bandwidth and Input Signal for Bandpass filter circuit
In general, you'd put a voltage source \$V_{in}\$ across your inputs, and analyze the network until you come to a complex term for the output voltage across \$C_2\$ dependent on the input voltage's (circular) frequency \$\omega\$.

Then you throw in your target filtering behaviour and find optimal solutions for the component values. It's an optimization problem, in the end.

However, in your specific case, I'd first reduce to either the first or the second stage first, and derive the frequency behaviour of that. Or, find it on common RLC literature and online calculators. You normally wouldn't want the R to be between the L and C, because that reduces the quality factor of your filter (your anti-oscillation idea still applies, just not like that).

You'll find that a single stage RLC filter doesn't give you very many degrees of freedom: basically, you can select the center frequency and a passband width, but in rough numbers, the transfer function will always only "decrease" with 20 dB/decade, so with two stages, you'd be very happy to get 40 dB attenuation at ten times the upper corner frequency. In practice, things usually are even worse.

For serious filtering, you'd go for LC-ladder filters (which can become unwieldy for audio frequencies), or for active filters (ask the analog.com website's filter designer tool ;) ). Or, just digitize the audio and do the signal processing in software – audio sampling rates are really no challenge to modern computing hardware, and if latency is not a concern of you, any couple-of-Euros USB sound card with a digitally implemented filter outperforms the frequency behaviour of an analog filter that wasn't designed without a lot of trial, error, improvement and costly revision.