It is incredibly boring and demoralising just training the learning skills first! It is better to have a plan to help you get a little out of the game while still training the learning skills (which are all important if you want to actually play with the big ships and the big boys.)
For the greatest level of fun (tm) use something like EveMon to help you create two skill queues to work out how to use two ships that suit your (hoped for) playstyle. If you fancy PVP (including piracy, faction warfare, nullsec/wormhole resident) or PVE (missions, highsec ratter/salvager) then I would suggest a frigate with weapon bonuses and then an assault frigate associated with your race.
EveMon will list all the skills you need to fly and fit the frigate if you pick a fitting from battleclinic, and it can suggest the training skills to make that training quicker. Stick to this skill queue!! Don't let anyone change your mind!! Start the skill queue in game, then go back to EveMon and do the same for the assault frigate.
If you want to train for a career in mining, then visit Halada's Mining Guide where he gives a great sequence of ships that you can spend time training for, gaining flying, mining and learning skills at the same time. Don't forget to train all learning skills to lvl 4 after the second ship.
For an industry career, train for a frigate with cargo space, then the various manufacturing skills.
For a trader, train for a fast frigate, then setup all the trading skills.
For an explorer, train for the frigate that has scan probe bonuses, then the four astrometrics skills in the science group should each be trained to level 4.
Once the first skill queue has completed, you can do lots of fun things in game while getting through the second skill queue (I would suggest earning ISK, as the second skill queue will not be as cheap as the first!)
When the second skill queues has almost completed, get EveMon to create a skill queue so you can train all the skills in the learning section to level 4.
If you do it this way, you can actually play the game during the first few days, as well as gain the learning skills that are so important for a long life in Eve Online.
(As noted in another answer, always always always train science to lvl 3 and cybernetics to lvl 1 at the very start. You can then use skill implants and boost your training time further!)
prefect
