Any pointers for beginners?
Off the top of my head:
* Do the tutorial missions. You can probably skip the research/production/planetstuff for now, but definitely do the combat missions. Not only will they explain what's going on, they'll give you I think 2 new ships and a couple skillbooks.
* Keep skills training 24/7. Skills continue to train while you're offline. Skillbooks to unlock skills you don't have can be bought on the market.
* Accept that sooner or later you WILL lose your ship. Many times. Maybe even daily. In fact, even during the tutorial you may get blown up a couple times. Don't get too attached, and any time you get into a ship that you would feel sad and not want to play anymore if it were to suddenly explode...insure it. No need to insure the very first ship you start with, but you'll probably want to be insured before the end of the tutorial by probably the second new ship they give you.
* Probably avoid lowsec at least for the first few days until you're comfortable with combat. When you do, expect to probably die, so don't take anything irreplacable with you. But...don't get "scared" of lowsec. The majority of the game happens there. Death is cheap in Eve.
* Missions will make more money than mining unless you have ships and training that you don't have yet. Don't worry about mining for your first few weeks unless it really fascinates you for some reason.
* Be sure to understand how clones work. You probably don't need to worry about it for a while, but if/once your learned skills become greater than the minimum "free" level be sure to ALWAYS have a clone. It might take weeks or months to get to that point, I really don't remember. But once you do get to that point, keeping a current clone is pretty much the most important thing, because if you don't you can permanently lose real time invested into skill training.
* Your life will be easier if you're within a dozen hops of Jita. It's the biggest trade hub in the galaxy. It's also sometimes laggy, so don't make it your home.
* Read mission texts. Sometimes they want you to do things that are non-obvious. Sometimes you don't actually have to fight anything, sometimes you have to approach objects to trigger events, sometimes you need to
not kill something, sometimes you'll be given a mission target that's of a certain object type that you might have placed in your target filter so you can't see it. In particular...there's an early tutorial mission that has you fly into an area and you'll immediately be bombarded by bad things that will kill you if you don't leave. You don't need to kill them. Just fly up then fly away and turn in the mission. Missions vary. Read them.