What makes a good ship?

I'm a relatively new player, only started about a week ago. I tend to flit from activity to activity, and I've been building ships with that in mind. A Keelback for mining, an Eagle for fighting, a Cobra for just messing around… I've been having good fun, but I haven't really dared venture far out yet. There's something immensely intimidating about the concept of such immense distance. I've stayed around my "home system" for most of my playtime.

Today, only an hour or so ago, I accepted a bounty hunting mission a bit further out than usual. I unknowingly jumped into my very first White Dwarf system. And I've never felt such wonder in a video game. Knowing that something like that is only a jump away… that's incredible. I've been out here mining asteroids and getting blown up dogfighting with AI and playing space trucker and it's been fun, but that feeling of awe I got as I took in my surroundings… I need more of that.

Problem is, building a miner is easy. Big cargo hold, hardpoints to hold your tools, space for limpet controllers,… building a fighter is a lot more complicated, but I manage. Building an exploration ship though… where do you ever start? What makes a good exploration ship? What makes a good ship in general? To what extent can you force a ship to do something it wasn't meant to?

I'd love to bring an Imperial Eagle into deep space, but I'm told that's not a good idea and I'm better off with a Krait Phantom or something like that. I just don't fully understand why.