Am currently finding the best exploration ship is the Sidewinder. I go back and switch ships if I need to do some work with a more capable ship.Why not just explore in the mining ship? It's not like you need jump range, a fuel scoop, AFMUs or hull repair limpets any more, since a carrier replaces all of those things. The best exploration ship is now a mining-rigged Cutter.
Welcome to the era of minesploration.