My favourite is the Corsair. It's pretty much a Phantom / AspX with the all-important enhanced SCO, which saves you a lot of time. I've explored a lot in a Courier, so I was right at home.
Currently though, I'd rank ships for exploration like this:
#1: Mandalay. It's grossly overpowered compared to everything else, there is no contest.
#2: Cobra Mk V. The enhanced SCO counts for a lot, and it's better for exobiology than the Mandalay (although not by a lot!), and it also has the second-best supercruise handling in the game, just slightly behind the Mandalay. (And both of them beat all other ships there, by a large margin.)
#3: Corsair. Its SCO enhancement isn't as overpowered as either of the above two's, while still being much more useful than not having one. Also, it can easily do a lot of speed and good shields while still holding on to a good jump range.
Then there's a large gap between these and the rest, because the easymode SCO saves you a lot of time when supercruising to distant places.
So, #4-5 would be a Phantom / AspX tie, #6 is DBX if you like exobio or Anaconda if you don't, and so on.
The Python Mk II and the Type-8 also have SCO enhancement, but they are thoroughly average in all other exploration aspects.
Oh, and about this:
(asking as someone who has no experience in those parts of the game so far, so idk what to look for apart from the jump range)
Let's see then... Supercruise handling (see
here), shield strength, for fuel scooping: the ship's heat characteristics, fuel scoop / FSD ratio, for exobio: landing footprint, acceleration, max speed. There are some other things too, like the number of internal slots, but every ship can carry everything that's needed there, even the tiny Sidewinder.
Then there are also subjective things, like how do you like the cockpit, the engine sounds, and so on. Personal preferences.