Combat Ship Skills Skills you'll want at Level III at least.

* Drones [Extra Drone Control]
      o Scout Drone Operation [+5km Engage Range]
      o Drone Interfacing [+20% Damage/Mining Yield]
      o Heavy Drone Operations [+5% Damage for Heavy Drones]
      o Combat Drone Operations [+5% Damage for Light/Medium Drones]
      o Drone Durability [+5% Shield/Armor/Hull for Drones]
      o Drone Navigation [Faster Drones]
      o Drone Sharpshooting [Increased Drone Optimal Range] 
* Electronics
      o Long Range Targeting [+5% Targeting Range]
      o Signature Analysis [+%5 Targetting Speed] 
* Engineering
      o Energy Grid Upgrades [-5% CPU for PDS, RCU]
* Gunnery
      o Gunnery [-2% Turret Rate of Fire]
      o Motion Prediction [+5% Turret Tracking]
      o Rapid Firing [-4% Turret Rate of Fire]
      o Sharpshooting [+5% Turret Optimal Range]
      o Controlled Bursts [-5% Turret Capacitor Use]
      o Trajectory Analysis [+5% Turret Accuracy Falloff]
      o Surgical Strike [+3% Turret Damage]
      o Weapons Upgrades [-5% CPU cost for Weapon Turrets]
      o Advanced Weapons Upgrades [-5% Power Grid cost for Weapon Turrets] 
* Missiles
      o Missile Launcher Operations [-2% Launcher Rate of Fire]
      o Missile Bombardment [+10% Missile Flight Time (More range)]
      o Missile Projection [+10% Missile Flight Speed (More range)]
      o Rapid Launch [-3% Launcher Rate of Fire]
      o Target Navigation Projection [-10% Target Speed Factor]
      o Warhead Upgrades [+2% Damage]
      o Standard Missiles [+5% Light Missile Damage]
      o Rockets [+5% Rocket Damage]
      o Heavy Missiles [+5% Heavy Missile Damage] 
* Mechanic
      o Repair Systems [-5% Duration of Repair Systems]
* Navigation
      o Evasive Maneuvering [5% Agility]
      o Acceleration Control [+5% Velocity w/AB/MWD]
      o Fuel Conservation [-10% AB Capacitor Usage]
      o High Speed Maneuvering [-5% Capacitor Usage / MWD]

Some other helpful skills deal with Electronic Warfare. These are skills that help neutralize your enemy. There's a whole set of skills that help with ECCM (Electonic Counter Counter Measures) but that's used mostly for PvP and since I'm dealing mostly with PvE newbies here, I'll just list a few that will help with missions.

* Electronics
      o Electronics Upgrades 1 [-5% Sensor Upgrade CPU need]
      o Propulsion Jamming 2 [-5% Warp Scrambler/Statis Web Capacitor need]
      o Target Painting 3 [-5% Target Painter capacitor need]

Notes: 1: Use Signal Amplifiers (along with Electronics and Engineering) to give yourself more Targeting Range and Scan Resolution (target faster) The Long Range Targeting skill also allows you to use the Sensor Booster to add more range and targeting speed as well. 2: Allows for use of Stasis Webifier I to slow down your target's speed and Warp Scrambler I to stop them from warping away. 3: Allows use of Target Painter I to raise the signature radius of your target to target it faster and do more damage to it with missiles.