I'm going to skip character creation, as I've only gone through it once and ended up choosing Gallente since that is the same race I choose when I created my character in DUST 514. I thought that maybe I'd be able to link the two somehow, but I never did figure out how to do that. I haven't picked up DUST since I started playing EVE so, I'm not sure it matters anymore anyways.
Everyone has a different experience with Eve, and that's a good thing. There is no text book that says you should do X,Y,Z and that's how you play the game. What works for one person may not work for another. You're going to hear all kinds of advice online and in the game, and generally everyone has a different opinion of how you should do the exact same thing. The advice that follows is my advice and my opinion based on my experience of only 21 days playing the game.
First off, I do recommended doing most if not all the tutorial missions at the starting station you begin at. I haven't done all of them yet myself but I think I've done about 75% of them. I recommend you go through these for multiple reasons. You'll earn 3-4 million ISK (money), learn the mechanics of the game, be given a bunch of free ships, and some of the core skills you need to get better skills later.
Speaking of CORE skills, it took me a week or two to even figure out what Certificates were and what purpose they served. Certificates are ultimately proof that you've mastered some level of a skill group. Nobody really cares about your certificates, but they provide good plans for deciding on what you should train for. There are various levels of each certificate; basic, standard, improved, and elite. I have 2 of the 5 core certificates right now and I'm working on the other 3. I have lots of other skills that don't fall into these core certificates, but I'm starting to find there is a lot of value in spending the time getting the first level of core certificates. Essentially, all the "Basic Certificates"; Core Capacitor, Core fitting, Core Integrity, Core Navigation, and Core Targeting, of which will give you the Core Competency Certificate.
I recommend you spend the time to work on this Core Competency Certificate because all the skills will set a solid foundation for anywhere you want to go in the future.