Agent level and quality level
Agents have 2 important attributes, called level and quality level. This leads to some confusion and this article attempts to clear up some of it.
Agent level
The level of an agent basically determines how hard the missions you get from it will be. Level 1 agents randomly select missions from a pool of missions that are a lot easier than level 2 missions.
You can complete level 1 missions in a well-fitted frigate. Most level 2 kill missions can be completed in a destroyer or a cruiser for the hard ones. You will need an Assault Frigate (AF) or a Battlecruiser (BC) for level 3 kill missions, possibly even a Battleship for the hard ones. And level 4 missions are hard to fly solo, even when piloting a Battleship (BS) or a Heavy Assault Cruiser (HAC).
Almost all level 2 missions will pay better than level 1 missions, but they're harder. Same from 2 to 3 and 3 to 4. Level 5 agents are not available.
Agent Quality Level
Every agent has a base quality, ranging from -20 to +20, which is listed in its info (base quality is also the quality listed in databases like EVE Explorerleaving this site). What's important however is the effective quality:
Effective Quality = Base Quality + (5 * Level of Negotiation) + Effective Standing
Effective quality (EQ) determines from what end of the mission pool the agent will select missions. The high the EQ, the shorter the trips will be for couriers and the closer the kill targets will be. Also, it seems to improve the chances of the agent offering the harder and more rewarding missions.
Note: this actually means that a higher quality agent may offer you harder, instead of easier, missions. The better rewarding missions are often the harder ones.
Effective quality also directly affects the reward and your standing gain with the agent and their corporation, for every mission.