Heavy Duty Armour mod : It's like a free present - all the benefits of the modification, and on standard lightweight armour, zero mass gain.
Lightweight Mount mod : Reduces the mass of weapons, with the possibility of additional weapons effects - if you game the game properly you can 'purchase' these effects and quickly regain Engineer rep for more mods.
Dirty Drive Tuning for your D-rated thrusters: these come with a heat cost but will turn your D-rated thrusters into something with a lot more oomph. The heat can be countered with...
Low Emissions Power Plant mod : helps lower your ship's heat - handy for fuel scooping.
Mods for Shield Boosters : various varieties, the more important one being for heat - get a bit more protection from heat weapons.
HD Armor - Good upgrade for lightweight alloys, but not a huge bump
Lightweight Mount - OK, but you won't be fighting anything successfully in a dedicated exploration ship. Good to have for the eventual "I discovered new alien gizmos floating in space... what happens if I shoot it in its stupid face?"
Dirty Drive Tuning - Terrible idea for an explorer. Dramatically increases power consumption (requires larger, heavier powerplant) and adds heat. Clean drive tuning is what you want.
Low Emissions Powerplant - Maybe if you get an awesome roll and don't lose any capacity. But you'll probably take a hit on PP output so you're back to needing a larger, heavier powerplant. I prefer to run an undersize A-rate PP; runs cooler.
Shield Boosters - Again, you're not staying to fight. Shield boosters just add unnecessary mass and suck power. A full set of countermeasures would be more useful since you will be running.