The Dramiel is the fastest Frigate in EVE.

The Claw is the fastest of the Interceptor group, but a Dramiel running an MWD is faster because of its lower mass, since MWD speed boost is affected by ship mass.

Things that affect speed are

• Base speed of ship
• Low slots (using Overdrive Injector II¹)
• Mid slot (using one 1MN MicroWarpdrive II)
• Rigs (using Small Auxiliary Thrusters II¹)
• Navigation Skill
• Acceleration Skill (when using the MWD)
• Ship mass (when using MWD)
• Implant bonuses (e.g. the Snake Set)²
• Leadership and Gang Assist bonuses²

Here's a table with the calculated speeds (base ship speed, max fitted/rigged and MWD, each without skill bonus and finally with all skills at level V³):

Here are the results as CSV. They were calculated from a subset of the CCP database export with this Python script, using the speed formulas from the top speed calculation guide and the Aenigma formula for bonus stacking penalties. Some calculated speeds were cross-checked against Pyfa.

¹ The speed bonuses from the Overdrive modules and Rigs are subject to severe stacking penalties, making it fairly useless to cram more than 2-3 of these in your ship in total. However for the purpose of finding the fastest ship it was assumed that all ships had their low slots full of Overdrive modules and their Rig slots full of Auxiliary Thrusters. This is not a sensible build to fly around in though.

² These bonuses affect the velocity directly and therefore don't matter for a ship comparison. They were not taken into account here.

³ Due to neither implants nor Leadership/Gang bonuses being applied, this is not the fastest these ships can go.

I've always thought of this as a bit of personal preference, but if you're looking at being a hardcore mission runner, a good suggestion is to pick a faction that has multiple Level 4 mission agents in a station. Additionally, since you gain standing with an NPC corporation more quickly than with a faction itself, multiple L4 agents from the same corporation in the same station is preferable. It will take much longer to grind up your faction standings to be able to pull missions from all agents in all NPC corps allied to a particular faction, so it's generally best to focus on running missions for that one corporation at first. Once you manage to get 5.0 or better standing with a faction, you'll be able to run L4s for any corp allied with that faction.

It is for this reason that I personally used to run missions for Theology Council in Amarr space. Theology Council has two L4 agents located in Sasoutikh, allowing you to pull multiple missions at once and run both of them before returning to station.

Next, if you're running missions you'll probably want to review a mission guide for tips on what ships will trigger new spawns and/or how to blitz the mission if your goal is to increase standing. Eve-Survival is generally regarded as the best mission guide around.

Lastly, don't take my suggestion of Theology Council as an absolute. It's merely the only system that I can think of off the top of my head that offers multiple Level 4 agents in one location. If you've got the time, I would encourage you to do some searching through the Eve Agent search to see if there are any other systems with multiple agents which might be better for mission running.