I have to chime in and recommend EVE University
as the first corp to join once you've done your tutorial, had a quick putter around and are ready to really learn how to play the game.
I have no affiliation with the corp, but know more than a few people The corp is 100% player run by experienced players who teach everything from PVP skills, ship fittings, industry, mining, missions, working as a team, etc. Their core purpose is to help noobs get in and up to speed, and will give you a huge leg up. I now fly with in 0.0 who have been in the corp, and have nothing but positives to say about them.
Another option if PVP is your thing is to get into a Faction Warfare NPC corp, get some cheap disposable fully insured frigates or cruisers, join some gangs and learn. Go onto BattleClinic forums
and read up on the "cheapfleet challenges" for some VERY cheap solid PVP fitouts. You will pop, multiple times - but every lost ship is another "ah, so if I had" or "i see what they did there" that builds your knowledge, and being around a FC and gang who know what they are doing is an excellent springboard.
From a personal perspective, I started as a miner in a mining corp about 4 1/2 years ago, and got so disenchanted I quit the game (and the lesson there is don't join the first group who invites you!). 2 1/2 years later, I came back to check out the new graphics (released a little over 1 year ago), bumped into some Aussies who took me for a spin in low-sec space for some PVP fun, and worked out what I REALLY wanted to be doing in game. Now live in 0.0, participate in PVP from solo through to 500v500 fleets, dabble in industry to keep some isk rolling in and to provide cheap goodies for myself and my corpmates, and enjoying my play time immensely. Sure the action isn't constant like a FPS - but I find PVP with real consequence (you die and the ship is gone - rather than just "meh, I die I'll just respawn and my gear comes back") gives you a real rush.