The answers depend on what speed you're operating at. Fast speeds go with small capacitor values, and fast recovery diodes.
If the capacitor charge is first positive, then negative...
then you cannot use an electrolytic.
Try what I do. Start at 1uF. Experiment with circuit operation, see how fast the capacitor charges and discharges. If it seems 'too slow', reduce the Farad value. Etc.
This is from the Navy Electricity and Electronics Training Series.
Module 9—Introduction to Wave-Generation and Wave-Shaping.
Page 117. Figure 3-17A.
www.hnsa.org/doc/neets/mod09.pdf
Although the text has an explanation, the schematic omits the toggle switching method.
To develop a working circuit, I made a simulation:
The capacitor values are chosen so they charge and discharge at what seems like a 'reasonable' rate.
Notice the transitions are not clean.
Operation is not always reliable. A toggle event needs to charge/discharge the capacitors, or else it puts the circuit in an unstable condition. As though it needs a moment to 'make up its mind' whether the left-hand transistor should conduct, or the right-hand.