Hello CMDR, I would D rate the sensors and life support to start. Then install two medium multicannons and four small pulse lasers. Open up with the lasers to drop enemy shields and then finish them off with the hull shredding multicannons.
Another good alternative, though maybe a bit more $$$ due to ammo costs, is four small SEEKER missiles, and two medium pulse lasers. Quite devastating that in my experience.
As for optional internals, go with the biggest shield you feel comfortable, a fuel scoop (the higher the rating here the better as it reduces refill time), a cargo rack, passenger cabin and SRV bay.
You might not be able to fit everything you want in one go, but I bet you can get pretty close. For utility mounts, maybe a Chaff Launcher, Kill Warrant scanner and Shield Boosters.
Should you fit shield boosters, IF YOUR SHIELD DROPS IN COMBAT, GO INTO THE RIGHT MENU UNDER MODULES AND IMMEDIATELY UNCHECK THEM/TURN THEM OFF in order to get your shield back faster.
Always, always, ALWAYS UPGRADE THE POWER PLANT LAST. I find outfitting everything I want first will give me an idea of precisely how much power I need. If you are close to the power you need but still fall a bit short, that's ok, go to Felicity Farseer and have her upgrade the power plant with the OVERCHARGED option. Even a level 1 or 2 will yield significant increases in output.
Don't forget to set the Cargo Scoop, Fuel Scoop, SRV Bay and FSD all to number 2 in the MODULES power hierarchy. This might help you as well when it comes to managing your MODULES when you are just shy of power to run everything.
I hope my advice helps and if you need anything, just ask. Fly safe Commander. The Asp Explorer is one of the staple ships in this game, she is a fine choice.