I can manage with just about any ship / team for the most part - but my favorites would be (in no particular order)

HD Harimau (If looks were a stat - this one is it.)
HD Qirex (Nothing like setting records in "that ship".)
HD Triakis (If you want to lose with style - that's the only way to go.)
HD Icaras (Yes my soul dies a little each time, but it is almost a requirement for time trials and such.)
HD AG-Systems (I hate it, I think it's ugly, and it's over-powered in acceleration / handling - but for some reason, I do exceptionally well with it especially on Phantom. See also dying soul from Icaras)

HD Auricom (In the end, my heart belongs to HD Auricom - it's my "home team" - and not many people like it. [That's a bonus in my eyes] If you can figure that thing out - it's very rewarding. Granted, winning in an HD Auricom is a LOT harder now that Fury ships are on the block, and side shifts are semi-broken again, but I still love it - aesthetically and functionally.