My first level 4 capable mission ship is the Caldari Nighthawk. I have not been able to find much information about this ship for use in missions, so everything contained in this post is my own personal experience.
Lets start with the fit I am using.
5x Heavy Missile Launcher II
1x Small Tractor Beam I
1x Civilian Gatling Railgun
2x Large Shield Extender II
2x Adaptive Invulnerability Field II
1x EM Ward Field II
3x Ballistic Control System II
1x Damage Control II
1x Shield Power Relay II
2x Medium Core Defense Field purger II
I chose to go with heavy missiles because the Nighthawk is really, really slow. Even with prop mods. The range of the heavy missiles allows the Nighthawk to reach out and touch everything within 60km. The damage is less than you'd get from heavy assault missiles, but HAMs have a vastly inferior range. So while the theoretical dps from HAMs is higher, in practice you'd waste too much time getting into HAM range.
The civilian gatling railgun may seem strange, but it does serve a purpose. Some mission NPCs are farther than 60km away from the mission warp-in. Having the railgun allows me to target NPCs in missile range and start applying missile dps, while at the same time gaining aggro on the mission NPCs out of missile range. Sure, you could always aggro them with a missile volley, but that wastes missiles. And why waste missiles when you can use a gatling railgun that doesn't need ammo to fire?
The tractor beam is there to loot wrecks and jetcans that contain mission objectives (such as The Damsel).
The mid slots are pretty self-explanatory. The Nighthawk is a shield tanked ship, so I chose mods that make the shield tank as strong as possible. The shield extenders nearly 7k extra shields, while the EM Field Ward boosts the incredibly weak EM shield resist of the base hull, and the 2 Adaptive Invulnerability Fields boost all the resists at once. This gives me a formidable tank that is not damage-specific. Over 13k shields, with resists over 80% across all damage types (when combined with the Damage Control mod in the low slots, of course). This can tank just about anything, except for the bonus room of the Extravaganza missions.
The Ballistic Control Systems increase missile damage and rate of fire. Having 3 of them doubles the dps output of the ship.
The damage control mod increases the resists of the shields, armor, and hull against every damage type. And its effects stack with the shield mods. It especially shines in hull resists; it gives 60% hull resists against all damage types.
The shield power relay and the medium core defense field purger rigs increase the recharge rate of the shields, which reduces the amount of time it takes to replenish your shields. Again, pretty self-explanatory.
I have been using this fit on my Nighthawk for several months now, and it works very well. Using tech 2 missiles, it can put out just over 600 dps, and with tech 1 missiles it can put out just over 400 dps. It tears through anything a level 4 mission can throw at it with ease.
There are a few drawbacks to this ship and fit. One weakness for this fit is that it is susceptible to NPC neuting. The tank is cap stable, but it can get neuted out fast. The ship itself is also affected by target jamming. Guristas are notorious for their perma-jamming. The other main drawback is that a good portion of the ship's dps comes from using kinetic missiles. If you are attacking something with a resistance to kinetic damage, switching to a different damage type may not be any better.
I will continue to play around with different mods to see if I can improve upon this fit.