The Asp Explorer's theoretical maximum is 38.19 ly, second only to the Anaconda. In practice, however, it will be less than that because of your outfitting.
This is my current loadout, which will be my first time going exploring since I bought Horizons. (I previously went exploring without Horizons but with a crappier FSD, so my range wasn't great.)
"Full tank" range of 33.6 ly will be good for most parts of the galaxy. As I near the rim or a diffuse region, I can extend that range a little bit by jumping on half- or quarter-tank (less fuel in the tank means a better jump range; just make sure you're jumping to a scoopable star!). Plus, I can use my SRV to collect materials for FSD boosting (already leaving the Bubble with a good number of boosts available).
In general the Exploration subforum is a great source of information for this. Check out the
Exploration Guides pinned thread by dognosh. It is a massive list of pretty much everything you might want to know about exploration. There is a "Builds" section, including links to several different Asp builds.
Pay attention to the different rationales that people give behind their builds. Some people want just range; others want to maximize the time between scooping; still others need good in-system performance or planetary landing capability. Always take your ship on a shakedown before you leave the Bubble to work out the kinks beforehand!
Safe journey, CMDR.