No, EVE is not F2P. Or, at least, it isn't any more F2P than it ever was. You can still buy PLEX with ISK... So, if you've got a steady revenue stream in-game, you don't have to pay for your gametime with real money.
The problem I have with EVE is similar to the problem I have with DF. Its sandbox-y nature means that things get boring after a while, unless you've set a good goal for yourself.
Everyone keeps saying that finding a good corporation is the key to happiness in EVE, but I haven't managed to find one yet. Seems like every corporation I join has a hell of a time getting anything done... And then falls apart after a few months. Very frustrating. Right now I'm just running around empire space in an NPC corp.
They say the new player experience is all kinds of wonderful now... Haven't tried it myself. I rolled up my character back in 2008 or so, and haven't revisited the new player experience since that time. So I can't say with any certainty there.
The nice thing about EVE is that you are never locked into one career path. You can start out heavily in mining (like I did) and then decide you'd rather be shooting stuff. The skill points you put in to mining are kind of wasted... But you just start training up weapons instead, and go shoot things. So, do whatever looks interesting to you. If you don't like it later, no harm.
I can't say I'd really recommend mining as a career choice... It's a halfway-decent way to get started. It'll get you some ISK, so you can get some better gear. But it really is pretty boring, and the income isn't that amazing. You can make better money, faster, doing just about anything else. Well, unless you really like mining and train all the way up into gas or ice mining... I hear those are pretty profitable. But I didn't stick with it that long.
I personally enjoy missioning... And salvaging is a great way to make cash... Exploration is fun, too, but I suck at scanning stuff down... Then there's all the manufacturing and trading stuff - never really got into that myself.