I normally have a favorite ship that I use for almost anything, but it changes from time to time. The Mamba is on top of my list, even though I normally don't use it for combat. I did Sag A* in a Mamba, and apart from the somewhat limited jump range (~40 ly), it's a magnificent explorer.
Currently I mainly fly:
Python: Core mining
FDL: Practicing fixed weapons
ASPx: Exploring/exploding
Vulture: "Little Walter" style fighting
Corvette: Bounty hunting and mat scavenging
Mamba: It's just the most pleasurable and exhilarating ship to fly in the game. Far from perfect, but way more exciting than all the rest combined.
Lately I've been thinking about building a ship to go to Colonia and see what life is like there. Then I would leave the rest of my ships at Jameson, so it would have to be something really allround, like a Python. Properly outfitted that ship will do anything. I would miss the Mamba though, so I would probably have it emailed to Colonia, but that ship and a Python would actually do the job