3 Websites every pilot should use...
Eve Survival: http://eve-survival.org
Specifically, the bit around Mission Reports. This site lists every single mission possible. It tells you exactly what will spawn and often provides pictures of the "rooms". It tells you exactly what tank to fit, what damage to deal, and will provide some strategy advice. It works nicely with the in-game browser. If you lose even one ship because you didn't know shooting the wrong mob would aggro the room it will only be because you didn't read the Mission Report. It may still happen, but just realize it was 100% preventable.
Eve Central: http://eve-central.com
Yes, I know you're going to say the market downloads are stale and they are, but it is still very useful as a fast way to check "general" pricing. Do not use it as the absolute tool of max profit. It isn't. But if you just can't remember if that skill book is 1 million or 3... Eve Central will instantly sort you out. Very handy for that price check in Jita, Rens, etc.
Ah I remember the days before dotlan... Maps were static and often out of date. It sucked and you basically had to memorize. Looking up things like true security status was nigh impossible. Now it is all totally easy for you new pilots. Dotlan is hugely powerful. Not only does it map out the systems, it can also provide one-click views to ship kills, station services, sov, moons, moon minerals, belts, and crap loads more. Later in life, you will appreciate the Jump Tool for capital pilots. Maps are essential for PvP roams. You can quickly spot "pockets", choke points, and backdoor routes for escape. Probably the most useful website in Eve.
There are dozens of other tools, but these 3 are what I would call "essential".