Your approach appears to be correct. Remember to divide your passband and stopband frequencies by your Nyquist frequency (here 125 Hz) to normalise them.
a. The fvtool graphics are telling you the characteristics of your filter, not the filtering process using filtfilt, that actually produces a maximally-flat-phase filter response.
b. The filter design you choose depends on the result you want. Your lower frequency (at 5 Hz) may make a Chebyshev design more practical, because you have a narrow stopband-to-passband transition in that region. An elliptic filter could give you the same benefits with that. A Butterworth filter can handle that, but takes a bit more effort to design. And then you have to consider the passband and stopband ripple you can tolerate, neither of which is a practical consideration with the flat passband and stopband of a Butterworth filter.
c. Whatever works best with your signal. Filter design (in my experience) is largely heuristic. I usually begin with a Butterworth design because of the flat passband and stopband characteristics. If I need a steep rolloff (for example as you do at the low end), and if the Butterworth filter cannot give the response I want, I consider a Chebyshev II filter because of the flat passband. Another possibility is a relatively high-order FIR filter (see the fir1 documentation).
Note that this is my approach. There is no one best approach, as there is no one best filter design. You have to decide what characteristics are most important, and choose the design that best meets your needs.
