I design Chebyshev first and second type filters
You are not going to see a lot of effect with this low order filters. If you want to study ripple and attenuation crank it up.
What are typical values of maximum ripple in the passband and minimum attenuation in the stopband? I struggle to find optimal value of those parameters.
This really depends on your application. You can pick something easy for starters: 1 dB ripple and 40 dB attenuation. That's probably not useful for a real application but at least you can make some graphs
I know that IIR filters are often unstable,
IIR filters are only unstable if the poles are on or outside the unit circle. Chebyshev are inherently stable unless you made a mistake. Implementation of a stable filter can indeed be unstable. That is heavily dependent on filter representation, topology, numerical accuracy and pole locations. A 6th order filters in scipy should not be a problem unless you are trying to use fix point or the cutoff frequencies are extremely low.