Opamp Astable Multivibrator - initial delay
Model 1 mV of offset voltage and this won't happen. The simulated op-amp is starting up in a precariously balanced-on-a-point condition that is totally unrealistic. 

To adjust the frequency, change R to a pot (better with a resistor in series). You can use a film capacitor. Ceramic caps are another possibility, but suffer from voltage coefficient (this circuit does not produce linear sawtooth anyway).

Note that period, not frequency, is linear in R as well.

For shaping to sine waves it might be better to use an op-amp + comparator oscillator, which will give you nice linear triangle waves, and can be adapted into a VCO which is linear frequency for input voltage by switching the integrator to +/- gain with comparator state.