The best thing to do is go to 0.0 to get the best gains, i've done this many times. You also need to train the 'Fast Talk' skill to get better gains for killing npcs.
Because there is a sec raise timer every time you kill something this means that you can only gain a sec raise every 15 minutes in one system, that is why you move between them.
- Find two (or more) joining 0.0 systems with plenty of belts.
- Warp to the belts looking for battleships only.
- Kill a battleship and LEAVE the other ships. (your sec timer starts)
- Move to to adjoining system.
- goto 2.
- After 15 minutes you can return to the original system to get another sec raise.
Now you're wondering why you kill only battleships and leave the other smaller ships? This is because leaving the others make battleships spawn faster so there is always something to kill or else you can wipe out whole systems of rats before they re-spawn. Also if when doing this you notice that the rats are taking ages to spawn, there will probably be an officer npc spawn which when killed gives very valuable drops.
Doing this method took about a week (5 to 6 hrs a day) to go from -10.0 to -1.8. I did it in a Drake and used about 20,000 heavy missiles.
NOTE: when in 0.0 be on guard, people will try and kill you!
The Sisters of Eve Epic Arc: Blood-Stained Stars
After you have completed the Tutorial and Career missions, you will have an opportunity to continue your missioning career.
The career agents will recommend starting the Epic Arc mission series with Sister Alitura in the Arnon system at the Sisters of Eve station. We recommend doing all of the career agent tutorials before heading off to the Epic Arc.
Some of these missions are difficult for rookie pilots. Many new players will lose ships while learning effective tactics to defeat NPC opponents. I recommend you fly cheaply fitted ships and insure with platinum insurance. The final bosses in the Epic Arc, Kristan Parthus and Dagan, can be very challenging for rookie pilots. Many pilots will get help by asking in local, although you risk having your mission objective stolen and ransomed by fleeting with strangers.
Information and tips on how to run some of the missions can be found on Eve Survival: Blood-Stained Stars
Further Missioning
The Evelopedia has a Missions Guide which can help you decide which corp and department you want to run missions for. Pilots who wish to mission close to the Eve University HQ in Aldrat often run missions for the Minmatar Mining Corporation in nearby systems. Other corps to mission for in nearby systems are listed in the Mission Guide to Aldrat.
I recommend declining kill missions against the four main empire factions (Amarr, Caldari, Gallente, and Minmatar) to avoid losing access to empire space. Having -5 or below standings with an empire faction can cause problems during war fleets, lowsec patrols, wormhole ops, and many other circumstances. This can also cause problems if you later join a corp that has their HQ in a faction's empire space that is denied to you, or if you join a nullsec alliance whose nearest empire space is denied to you. When you have -2 or below standing with a faction, only the Level 1 Quality 0 agents and below will be available to grind standings, which could be a lengthy process.
You can check mission information before accepting or declining on Eve Survival. If you want to find agents close to a particular system, you can use the Agent Rangefinder web application. There is a database of agents available on the Eve Agents website. Some of the entries are outdated and you should always check in-game to confirm the existence and location of the agent. You can also use the map to see systems where you have agents available to you. Open the map (F10), go to the Star Map tab, go to the Stars sub-tab, go to the My Information section and select My Available Agents. Flattening the map can make it easier to navigate. Hovering your cursor over these star systems will list the available agents along with their respective corporation, level, quality, and division.
Career Choices
Although most players start making ISK in EVE by running missions, there are plenty of other ways to make a fortune. The Tutorial Agents give brief insight into some of the many careers in EVE. You are not restricted to the list below, but here are some popular choices:
- Ratting - Killing NPC pirates("rats") for bounty rewards and loot.
- Exploration - Archaeology, salvaging,
- hacking, as well as running deadspace complexes and wormholes.
- Mining
- Industry and Production
- Trading and Hauling
- Piracy
Best Answer
It doesn't talk about specific ships so much, mostly general tactics, but this is still a good article about taking on pirate cruisers :
http://www.evealtruist.com/2011/11/know-your-enemy-pirate-cruisers.html
I believe it's still valid advice at the moment, but it may not be when the pirate cruisers get rebalanced in an upcoming patch.