EvE online, you don't have the stuff
I figured since I've been playing for almost a week now, I'd post my thoughts on being new to this game.
It's really not as hard as some people say. There are very in depth aspects to the game, and if you want to get into that you can, but I haven't had any problems catching on. The career path missions at the beginning are very good at showing you exactly how to do everything. I still have the advanced military one to go through, but that's it. You really can spend as little or as much time as you want with the game. You can do just fine as a casual player.
You get at least one ship as a reward during each of the paths, along with plenty of equipment to outfit them with. I think I had 7 or 8 ships before I decided to start selling them off. Necronic dropped me a good chunk of change to get me started with, but I haven't even touched it yet. I want to make sure I know what I want to do before I go nuts and start buying stuff.
I'm not a huge fan of combat, and in this game that's OK. I don't have to spend my time blasting pirates. Sunday I spent most of my time just scanning different systems seeing what I could find, and trying to find out how to place my probes to get objects scanned down quicker. I found a ton of wormholes, some asteroid fields, an old wrecked pirate instalation, and some pirate hideouts. I haven't made much money off of it yet, but I have a feeling as I get my skills higher and my ship upgraded I'll be able to cut a bunch of time off of scanning and be able to jump around quicker to different systems looking for what I want. You wouldn't think it would be that entertaining, but I like it.
The biggest thing to get used to is the idea that you can lose a ship so easily. To me it adds so much to the game though. The idea that your losses are permanent. Don't cry to the GM about someone who screwed you over because they will probably just laugh at you. You are responsible for your own stupid decisions.
The look and feel of the game is also completely different than I have seen in an MMO before. The graphics are great, but that's not really it. In WoW you run around Orgrimmar or Dalaran, and there's a bunch of lvl 80's all with high end gear running around dancing on mailboxes and they all are "Champions". In Eve it feels a bit more restrained. Maybe it's the thought that cocking off will get your pretty new ship blown up.
TLDR - Freedom to do what you want, meaningful consequences, and an environment that makes you actually think about what you are doing is what I'm liking about this game. I'm only a week in, so it's just an initial reaction, but I'll be dropping WoW for this game.
If you get yourself into a good corp (take some research) other corp may not touch you since they worry about corp retaliation. 
It was on the last mission of the advanced military training. Wasn't expecting what they dished out. I finished it on the second try, and got a free destroyer out of it, so I made it out ahead.