I'll list these in a general order of training. A key note: Training to your racial frigate and gun type of choice is always a good first day of Eve approach, as it will let you actually do something in game. It may also be worth training a few levels in the racial cruiser and medium turret or missile too, but that is by no means an absolute. It just gives you a few more ships to play with early on. Also, playing through the tutorial missions will get you many of these skillbooks for free, so it is worth sending a day or three doing those missions!
Core Fitting Skills
These are horribly boring, but are highly useful as you start trying to actually fit your ships.
Electronics - Targeting, EWAR, and CPU based skills
- Electronics 5 - 5% CPU per level
- Electronic Upgrades 3 - Opens up a wide variety of useful modules for fitting
- Targeting 5 - You can never target too many things
- Multitasking 4 - See above
- Signature Analysis 4 - Target faster
- Long Range Targeting 4 - Target further
Engineering - Powergrid, Capacitor and Shield skills
- Engineering 5 - 5% powergrid per level, opens up shield tanking skills
- Energy Management 4 - 5% capacitor per level
- Energy Systems Operation 4 - 5% capacitor recharge per level
- Energy Grid Upgrades 4 - reduces CPU need of many fitting modules
Mechanics - Armor, Hull, and Rigging skills
- Mechanics 5 - 5% hull hp increase per level, opens up many other skills
- Hull Upgrades 5 - 5% armor increase per level, opens up armor tanking abilities
- Jury Rigging 3 - Opens up most other rigging skills
Navigation - Speed and Agility
- All of the skills in this division that do not start with "Jump" are extremely useful and should go to 3, probably 4. These all make you move faster, turning faster, and useless capacitor while doing so. Moving faster is always better!
- Weapon Upgrades 4 - Somewhat mysteriously placed in the Gunnery tree, this skill reduces CPU requirements of almost all weapons in the game, and as such it is useful to all pilots.
Training the above skills as a start will make it easier to fit and fly almost every ship in the game! The results are not readily apparent when you queue them up, but getting those done sooner than later makes using every hull you sit in better! What you train next will in large part depend on what weapon platform you are leaning towards, Turrets or Missiles, and what tanking style you will use, Shield or Armor. I recommend tanking skills first, but that is a personal preference. Listed below are the core tanking skills in each subset. I recommend taking all these skills to 4 in roughly the order shown.
Shield Tanking - In Engineering
- Shield Management - More raw shield
- Shield Operation - Faster shield recharge time
- Shield Compensation - Reduces cap need of Shield Boosters
- Shield Upgrades - Reduces powergrid need of most shield modules
- <Damage Type> Shield Compensation - there are four of these, for each damage type, and they improve your resists.
- Tactical Shield Manipulation - While not mandatory, stops some damage from leaking into armor when you shields are low
Armor Tanking - In Mechanics
- Repair Systems - faster Armor Repair cycle times. Mandatory, take it to 5 if you can wait that long
- <Damage Type> Armor Compensation - Works the same as shield compensation skills.
You may notice that shield tanking seems to have more skills. You are somewhat right! Armor tanking is in large part dependent on your capacitor and fitting skills, and Hull Upgrades, which you already trained, opens up armor plates. Also, armor tanking uses low slots, and often negates the use of damage upgrades, so my theory is that there are less skills to offset that "penalty". Also, shield tanking allows passive setups that still regenerate hitpoints, while passive armor tanking does not. For a very nice guide to tanking, and to skills and Eve in general, I highly recommend you check out Isk: The Guide.
If you have trained this far, you are probably already learning what you want to train next. Past these basics, which I consider the core skills of Eve, you desired play style will influence the ships, weapon skills, and other support skills you will want to train. I'll probably cover the weapons skills in the future, but for it will suffice to say Amarr, Gallente and Minmatar pilots will want to focus on Gunnery for turrets, while Caldari and some Minmatar pilots will want to focus on Missiles for... missiles.