It's really going to depend on what you want to do with it, but since it's a fighter by nature (and the sidey's probably better for anything other than combat) I'm going to answer assuming you plan to do some bounty hunting/combat missions.
I would begin with getting a weapon in your third hardpoint. I run a gimballed muticannon which pairs well with two fixed pulse lasers (was running fixed burst lasers, but had to give them up because of power needs elsewhere). Once you've got three weapons, I'd look at thrusters or the power plant next, but both get pretty expensive for even the C rated stuff so it may take a little saving. Definitely get a Shield Cell module at some point, the Eagle is somewhat paper-like before you upgrade the shields and hull plating (and somewhat construction paper-like after) and I can't tell you how many times the cells have turned what should be a 30k insurance cost into a 4k repair cost. Although I have an open internal slot, I skipped the scoop to keep weight down - I do have to stop for fuel fairly often, but it's a good time to turn in the bounties I've built up since the last refuel.
Bottom line though, there's really no "correct way" - it's all about what you think might be more useful to you based on what you plan to do. Considering a pilgrimage to Sol to see the cradle of humanity? Maybe an FSD upgrade should be prioritized to cut some time off the journey. Just keep whatever goal you've set for yourself in mind, and upgrade as you see fit.
Fly safe, Cmdr!