My first "exploration" ship was indeed the DBX, bought for long distance Buckyball races back when a ship that could jump 35 ly fully equipped was something remarkable, and the Hauler and DBX were a racer's top choice. Loved the sound and its general feeling of flying a small truck, but that tiny fuel scoop will get to your nerves on a proper exploration tour eventually.
The "Bucket Of Bolts" became a 60+ ly monster over the years, I still use it from time to time when I
really need to reach a distant place fast, but I'd never use it for real exploration purposes. I play for the visuals as much as for the actual gameplay, and the DBX isn't exactly a screenshot diva to my eyes

.
When I finally decided to embark on some real, done on purpose exploration, I bought the AspX, since that was
the exploration ship. Went around a bit with it, but something didn't really click. A great, efficient ship, good at everything I did with it, but in the end just "a ship", lacking that kind of character that made it feel "my" ship. Still have that one as well, but it has largely been superseded by the universally mocked Scout sibling. I do with it the same things, but it's more fun to fly and I like its rear exhaust arrangement more for screenshots. Also, almost everyone will look funny at you, especially after wasting Arx on limited premium paintjobs for the Notredame hunchback of ships, so absolutely bonus point for that.
And anyway, after having said all that, my first trip to Colonia and only trip to Sag were made with a 17 ly-capable T-7, and my "official" exploration ship with which I traveled the most distance is an Orca (great range, great panoramic view except downward, great speed and agility for its size, looks great in low-fov screenshots), so really don't take any advice from me, just enjoy what you enjoy the most.
(Dolphin will probably make the best all-round small size explorer: its really just a tiny Orca that can land anywhere and scoop literally inside star nuclei with impunity, since they utterly botched its heat dissipation with an update from a couple years ago)