You don't necessarily need a good Asp to explore. I've been doing a lot with a upgraded Cobra (2.5 mil in it). Even with only a 15-20Ly jump range there is a lot you can explore. Also I would buy power plants based on how good they handle heat. My cobra's PP doesn't give the most power but it handles heat the best. The Heat Sink Launcher module, is a good way to do an emergency heat dump if you get too close to a star for too long.
So a tip some folks may find helpful. I had worked myself up to a Cobra without trading but really wanted an Asp because I heard it was great for exploring. I found that by equipping my Cobra with some cargo space and spending a few hours focusing on trading rares, and doing some scans between the stations selling rares, I was able to earn enough fairly quickly to make the upgrade in ships and also not feel too much like a trader.
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