What are the various ways to choose bonds for a butterfly strategy? For eg., I already know the most common one i.e., choosing short and long term for the wings (barbell) and the medium term for the body (Bullet).
It really depends on what you're trading on.
Very often, butterfly trades are simply mean reverting trades. For example, you may look at 2s/5s/10s (typically on a regression or PCA-weighted basis) and see whether it's trading at "extreme" levels relative to history (i.e., are 5s trading rich or cheap relative to where 2s and 10s are trading). This can be done for any butterflies, as wide as 5s/10s/30s, or as narrow as Feb17s/Aug17s/Feb18s.
Other times, butterfly trades are convexity trades. For example, 5s/10s/30s duration neutral barbell would be a long convexity trade (because 30s are far more convex than either 5s or 10s).
Butterfly trades could also be macro or Fed trades. For example, if you believe the fed will keep the front end of the curve anchored in the near term, but future growth outlook is improving very dramatically, causing the belly of the curve to underperform, then shorting a 2s/5s/10s butterfly would make a lot of sense (this kind of trades worked very well this year).