I think starting as a new player now is entirely different to starting a few years back. Even when I started in 2009, there was a structure of introductory-like missions in various parts of the game, which have been expanded significantly (as far as I'm aware) since.
An account by default has 3 character slots. Up until recently only one character could be training skills (in realtime) at a time. Now there is potential to have 2 of them (perhaps all 3, I am unsure) training at once, but it involves paying for it (via in game, or real life cash). To be honest, I find one character is easily sufficient, having a second just splits useful training between characters.
(Unless you have an entirely alternate account)
There's a tonne of stuff to do for both playing actively, or more sedately. Mining is probably the initial choice for more sedate playing, as it has a low SP entry point and you can do it in one of the initial frigates (though of course, it's equivalent to mining in an M4/M3 in X3)
Mooching around high sec space scanning down dynamically generated points of interest I find quite easy going, as it's mostly just zipping about and exploring. Sometimes you'll find some rats, but being highsec they shouldn't be overbearingly tough. You can also find extra asteroid belts by scanning which might have less common ores in too. (I'm not a miner myself mind)
Other activities like trading are possible, but need large isk backing to make work, I think. It's not something I've gotten into, because even now I wouldn't say I know the market well enough to take big gambles except with a very few items I know kind-of-okay.
For active play to begin with, every NPC corporation has agents who offer missions (typical quest-style stuff). These can also be fairly laid back (eg, courier or mining missions) but can also be "go here and kill this stuff." The latter is how I make a pretty significant amount of my money still, as sooner or later you get to a point where these can be completed fairly easily for a solid, low risk, reasonable reward income. (Many still think high level missions still pay too much for the small risk involved in fact)
Much later, once you have some isk and proper skill training under your belt, incursions are dynamic combat missions which have a view to pay very nicely. They're tougher than typical combat missions from agents, and need to be done in a group (solo is neither a reasonable idea, or worth it, as the reward is scaled depending on the number of participants) but the potential income if you get into a good group is a big jump over other high sec combat activities (in my experience so far).
There's also other stuff out there I don't know too much about. General industry is obviously a big business, but I don't do much except a few T1/T2 rigs, so couldn't comment on how easy it is to get into.
As a new character you can expect to be dropped into high-sec empire space as part of an NPC corporation and minimal stuff - not too dissimilar to a new X game. When I first started I think I made good use of the
evelopedia, and another site I hear is useful are the Eve University pages.
After that, once in game there is a "rookie" channel open for general noob questions for people starting out. Your initial NPC corp chat will also likely be full of new players who might be able to help you out - but you should consider finding a player corp that suit your interests quite fast.
First: They have an invested interest in helping you out, no one else necessarily does.
Second: There's a good chance a player corp tax rate is much lower than the NPC corp default of 11% -> that's a tax charged on every transaction, bounty, and mission reward you get.
Third: EVE really is a social game. The more people you know and get on your goodside, the better. While EVE is infamous for tales of players totally screwing one another over, it's actually much more common that you'll get offered "mates-rates" by your corp members, or even just gifts to help you get started. (Many larger corps offer schemes for training new pilots, and ship replacement setups)