I will be going to Miami (USA), then next day to Colombia and while coming back I will be staying in New York for 3 days. Should I apply for a transit visa or a B1/B2 one?
For the outward bound connection in Miami to Columbia, a C-1 transit visa would suffice. However, for the stopover in New York on your return journey, you would require a US B-2 visa which allows for visit with friends/relatives, vacation, sightsee, etc.
A transit visa (C-1) is not intended for visits, but rather for a continuous journey through the US, including any layovers for a connecting flights.