Railguns. LOL.
They're freaking awesome, although overkill for such a small ship.
I've had the most fun going for kills. It was the most lucrative route too - the Sidey is just too small to trade in, imo.
I'd go for lasers if you're worried about costs and/or rearming if you're light years from an inhabited system. In all honesty, though, I'd suggest that multicannons are better - they do less damage to shields, but tear big chunks out of the hull once you get through, and a Sidewinder isn't the most obvious choice for an explorer.
If your aim is crap, go for gimballed weapons. They're more forgiving. I had some success with two gimballed multicannons.
I can't remember what else I had in terms of reactor, power distributor and shields, but they were all significant upgrades. The distributor was A1, iirc.
As I'm still sore from the experience, I suggest that you avoid the cr100,000+ kill missions for the time being - I bit off more than I could chew tonight in my first mission of that kind (in a tricked-out Viper). The target was in an Anaconda. He cut through my shields like they were butter in one pass, and quickly disposed of the rest of my ship. I didn't even have time to target any sub-systems to slow him down.