It obviously depends on your budget, and tastes.
In the 'small to medium' category, popular choices are...
DBX: cool as ice, no need for heat sinks, small and easy to land, 2nd greatest jump range. Pretty good cockpit, a bit slow scooper.
AspX: 3rd greatest jump range, great canopy, great agility in supercruise, solid number of internals, drifts a lot in normal flight.
Dolphin: Agile and fun in normal space, good canopy and agility in supercruise. A no-brainer to drag a rich explorer to a corner of the galaxy.
Type-6: Less obvious (slightly worse jump range than the others) but very cheap to outfit compared to the others, great cockpit, internals outdo an Aspx, very small footprint to land, easy to fly in normal space.
In the 'heavier' category, ships able to carry more internals. I would list...
The Orca: Slightly better jump range than the Dolphin if done right, and more internals (pricier, obviously) crazy fast in normal space.
Type-7: Lesser used as the jump range is slightly lower, but astounding number of internals for its price.
Anaconda: Pricy, but valued for having the best jump range of any ship if setup right. The agility in supercruise is abysmal, and the cockpit doesn't have a grand view however.
The Krait is gaining in popularity - lots of internals, jump range competitive with a Dolphin/Orca, and the ability to carry a SLF. Also it has a remarkably clear cockpit, and an espresso machine.
Exploration being quite casual, one can go out there in -any- ship really. (I have a friend with a 40+ light year clipper, thanks to guardian boosters) But for maximum comfort, plan for a SRV bay, both scanners, an AFMU, a solid fuel scoop. A small shield OR a combo of a small repair limpet and cargo bay. That means 6 internal slots.
Oh, if you want to nab stuff from the guardian ruins, I recommend the smaller-footprint ships. Dolphin, Type-6 or DBX.