I mostly run missions for the Gallente, although I did a stint for Cal Navy to get jump clones. I have flown the following ships in level 4 missions fairly extensively:

Gallente
- Dominix - easy to fit, easy to fly, but it took too long to get anything done. I didn't have great skills at the time, so one of these days I might have to give it another go
- Megathron - Antimatter rails sniping setup. A lot of fun at long range, no fun at all at 5km :-)
- Ishtar/Eos - More fun than larger ships, and great tanking against K/T NPCs, but the DPS wasn't high enough to grind missions effectively

Amarr
- Abaddon - Can be fitted to be practically indestructable or a damage dealer, and being able to change effective range from 15-50km is very, very nice.
- Dual perma-rep setup and rat-specific hardeners can take any level 4 mission I have done (eg WC) forever, but the DPS is terrible.
- Can also be set up with a weaker tank and decent DPS, although you're still limited to EM/T. This is my staple set up, as I've found it can either slice through or tough out any mission I throw at it with minimal fitting changes or expense (eg ammo). Mine has had a chunk of hull missing for about a year as a reminder of the time I forgot to read a mission description properly and fitted the wrong hardners (Oo)

Caldari
- Drake - fantastic ship for the ISKies and low-SP requirements. Can't solo tank lev4s without careful fitting and good skills, but can do respectable damage and survive long enough
- Raven - Bog standard active tanked Raven setup with cap control circuits. It gets the job done, but I was disapointed by the tanking with just T2 gear
- Nighthawk - Can passive tank really nicely, good DPS and can use multiple damage types, although the bonus to kinetic means it's rarely worth using anything else. //Really// fun ship to fly, although it seems to take forever to reload missiles when you're used to crystals