  We describe a general analytical framework of a nanoplasmonic cavity-emitter
system interacting with a dielectric photonic waveguide. Taking into account
emitter quenching and dephasing, our model directly reveals the single photon
extraction efficiency, $\eta$, as well as the indistinguishability, $I$, of
photons coupled into the waveguide mode. Rather than minimizing the cavity
modal volume, our analysis predicts an optimum modal volume to maximize $\eta$
that balances waveguide coupling and spontaneous emission rate enhancement.
Surprisingly, our model predicts that near-unity indistinguishability is
possible, but this requires a much smaller modal volume, implying a fundamental
performance trade-off between high $\eta$ and $I$ at room temperature. Finally,
we show that maximizing $\eta I$ requires that the system has to be driven in
the weak coupling regime because quenching effects and decreased waveguide
coupling drastically reduce $\eta$ in the strong coupling regime.
