The integrator method will produce a triangular waveform, not a sawtooth...which one do you really need?
The easiest way to produce a sawtooth is with an UJT (unijunction transistor) oscillator, which consists of exactly three components: the UJT itself, a resistor and a capacitor.
The circuit can be further enhanced with another resistor on base 2 for temp stability, and if you want the sawtooth to be really linear, with a current source instead of the charging resistor. You can roll your own or use a LM334 in a temperature compensated configuration (see figure 15 in the datasheet).
Lastly you need to buffer said sawtooth, in which case the LM324 is a good option (as long as you keep the sawtooth at a low frequency, say 200 Hz max). At higher frequencies you may want to use a TL074, or any other opamp with a higher slew rate.
Since the TL074 is a FET input device, it will load your circuit far less, and therefore that would be my opamp of choice even if I were generating low frequencies.