Postby Xebeth » Sat Oct 15, 2016 9:45 am
Let me start my answer with a friendly warning, if you focus solely on the big ships like they are some sort of end game prize, you will in all likelihood turn the game into a grind, become frustrated, and will ultimately be disappointed. The 'best' way is to do what you most enjoy doing, and eventually you'll get there, and have a lot more fun on the way.
Ok, with that out of the way, there is a lot of information missing from your question, how long have you been playing? What do you like doing? What ship(s) do you currently own? How many credits do you currently have?
The quickest way it to probably grab a ship with a decent cargo carrying capability (and a fuel scoop) and do a bunch of Sothis/Ceos runs (a couple of adjacent systems out on the edge of the bubble that pay multiple millions for hauling biowaste a few hundred lys), the process is dull and repetitive, but does come with the added side effect of quickly increasing your trade rank.
If combat is more your thing, then RES (resource extraction sites) are your friend, if you are 'good' at combat hit up the Hazardous ones.
The right missions can actually pay quite well, but you'll need to work on your reputation with the local factions as the highest paying ones come with the highest reputation. You are going to have to do this anyway if your eventually want the Corvette as it's locked behind federation ranks.
Exploration probably has the worst credits per hour, so unless that's a particular passion I'd avoid it if expediency is a real requirement.

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