1) Open Character Sheet.
2) Open standings.
3) Scroll down to corporations, click the top one. If corporations is just about empty you can also follow the same procedure for the top faction and pick a good sounding corp within it (if you want kill missions you should be able to find one that sounds as though it gets involved in combat).
4) Click the agents tab.
5) Expand the list, and it will show which agents are available to you.
Do enough missions that your standings get high enough that more agents become available to you. If this is happening too slowly for you train the 'social' skill to gain standing more quickly and train the skill 'connections' for a percentage gain on your current level of standings. Having zero standings before skills and connections at 4 used to enable you to access minimum quality level 2 agents without having done any missions at all; now you will have to do at least one or two.
Use the best agent you can for the level you can safely complete. Agent quality has no reflection on mission difficulty, just on your rewards for it. For mission types see bio info below. Also bear in mind that lower security systems give better rewards, but once you are into .4 or below you can be shot at by passing players too. Agents close to lowsec space but not in it may ask you to go there once in a while, don't forget you can always turn down one mission every 4 hours, but if an agent is doing this a lot it might be worth looking at a change of agent. If, on the pther hand, you prefer the rewards of missioning in lowsec find an agent deep within it to be safer; it's the border between high and low that carries the most risk.
For a database for comparing agents across eve I recommend the database at eveinfo.com under links, out of game. Alt-tab is your friend!
Administration: 50% Kill, 50% Courier
Advisory: 34% Kill, 66% Courier
Archives: 5% Kill, 90% Courier, 5% Trade
Astrosurveying: 40% Kill, 30% Courier, 25%
Command: 97% Kill, 3% Courier
Distribution: 5% Kill, 95% Courier
Intelligence: 85% Kill, 15% Courier
Internal Security: 95% Kill, 5% Courier
Legal: 50% Kill, 50% Courier
Manufacturing: 5% Kill, 95% Courier
Marketing: 5% Kill, 95% Courier
Mining: 5% Kill, 85% Courier, 10% Mining (II)
Production: 5% Kill, 95% Courier
Public Relations: 34% Kill, 66% Courier
R&D;*: 0% Kill, 50% Courier(S), 50% Trade
Security: 90% Kill, 5% Courier, 5%Trade
Storage: 5% Kill, 95% Courier(L)
Surveillance: 95% Kill, 5% Courier