The Adder. Can't go wrong. 27ly jump range. Cheap to repair incase of any mishaps(which WILL happen). If you run into a problem with the ASP you will pay through the nose for it, making you regret it.
Make it light as possible. Don't need any hardpoints including weapons. Just the barest equipment.
Fuel scoop, basic discov scanner(it's fun actually discovering planets and not being given them on a platter) and detail surface scanner. That's it. Downgrade everything else to make your vessel lighter.
One thing worth mentioning is that flying the Adder makes you feel like an explorer. Smallish windows to peek out of, and the lighting inside the cockpit is just gorgeous. Makes me feel like coop from interstellar. It's incredibly immersive.
But yeah, I would choose the Adder over the Cobra(for exploration) anyday.