First 200 hours in EVE

When training skills in EVE, the sheer number of options available can be overwhleming. In order to introduce new players to a few facets of the game, as well as the skill training mechanics, I've produced a very generic annotated skill plan.

The plan should run about 200 hours (about 8 days and change), leaving the new player in the second half of their free trial flying a cruiser, and free to experiment. Also note that, based on the skills recieved at character creation, some of the goals may already be achieved. Lastly, this skill plan is not meant to be optimized or ideal, but rather a broad introduction to the world.

General Skill Training Methodology

In the interest of space, the skill plan below will list off the desired level for a skill, i.e. "Afterburner III, Engineering III." Note that, because of the progressively-longer skill training times, it's typically best to stagger skill training. Thus, in the case above, the character is encouraged to train Afterburner I, Engineering I, Afterburner II, Engineering II, Afterburner III, and finally, Engineering III. This allows your character to improve at a more steady pace.

Starting Out: Let's Kill Stuff

The first order of business is to improve our ship and our combat skills.

Racial Hybrid Turret III: Every race has its turret, and training it up to level III will help improve the damage output. You may also choose to train the Missile Launcher Operation and Rockets skills in addition or instead of turret skills.
Engineering III and Electronics III: These skills make fitting modules onto ships much easier, and are important to get early.
Repair Systems III or Shield Operation III: You'll take damage from enemies, and you'll need to repair that damage during combat, known as tanking. Repair Systems repairs the armor of your ship; Shield Operation repairs the shields.

Learning to Learn: Skill Training Faster

Every skill is tied to two attributes. These attributes directly affect how fast the skill trains. Naturally, you'd want to boost those attributes. And since buying +5 implants is out of the question, let's go train some learning skills.

Instant Recall II
Analytical Mind II: In an exception to the "staggering" advice I gave before, you'll want to train Instant Recall completely to Level 2, THEN train Analytical Mind to Level 2, then lastly train the remaining two skills in a staggered manner. Why? Because they affect the attributes that determine how long Learning skills take to train, so getting them to their top level ASAP is critical!
Spatial Awareness II
Iron Will II: Why not more? Because Learning skills aren't fun. And because there will be plenty of time to train them later on.

Note that there are a LOT of characters with +9 attributes because of Learning and Advanced Learning skills. It's a long and boring journey. But millions of skill points later, I can't really complain.

Come See the Softer Side of EVE: Mining

All of those ships that the pirates and soldiers lose have to be replaced somehow. And there is NO NPC influence on the mineral market, so building materials have to be mined or bought. There's no shame in being a carebear. As a matter of fact, there can be a lot of ISK in it.

Racial Frigate II: Every race has a "mining frigate" that requires the racial Frigate skill at Level 2. Look for the bonus to mining laser yield in the description, and you've found it.
Mining III: Make your mining lasers work harder.
Hull Upgrades I: As you drag ore in, you'll need a bigger cargohold. Hull Upgrades allows you to fit Expanded Cargohold modules.
Refining III: Lastly, you'll want to be a bit more efficient at transforming your ore into minerals. Then again, you might get a better return on selling the raw ore, so do a little bit of market research and gasp math!

Versatility: Expanding Your Options

Now that we've got a bit of experience, we can start to broaden our horizon, and see how the "support" skills are as important as the prerequisite skills.

If you're interested in using guns in combat, train:

Controlled Bursts II
Rapid Firing II: Your guns will fire faster, and take less capacitor.

If you're interested in using missiles in combat, train:

Missile Bombardment II
Rapid Launch II: Your missiles will fire faster, and have a longer range.

If you're interested in drones, train:

Drones II
Scout Drone Operation II
Combat Drone Operation II: You'll be able to control a pair of light or medium scout drones (if you have a ship with a drone bay), and their damage will be boosted slightly.

If you're interested in mining, train:

Mining IV: Tech 2 Mining Lasers!
Trade II
Broker Relations II: Sell more of your ore and minerals on the market for a lower cost.

Bigger, Stronger, Slower: Cruisers

The last part of the plan is to get behind the wheel of a cruiser. You'll still be using frigate-sized guns (which isn't neccessarily bad), and cruisers can be expensive, but they'll allow you to fight harder enemies, carry more cargo, mine more ore (if you're Caldari or Matari), and see what bigger ships feel look like.

Racial Frigate IV
Racial Cruiser I: Once you have the ISK, either through mining, killing NPCs, or friendly donations, go find a cruiser to fly. Caldari and Matari get the Osprey and Scythe, repectively, which are outstanding mining cruisers. The other cruisers range from glorified cargo haulers (Exequor) to powerful combat ships (Maller). Do some shopping for the cruisers your race provides, train the Cruiser skill up a bit more if neccesary, and enjoy the second half of your trial period!