There is so much depth and so much going on in EVE that the learning curve is huge. It's amazing though. If you are going to get into it I suggest convincing a friend to join you. Half the fun in that game is flying around looking for people to shoot or trying to get somewhere and desperately hoping you don't run in to a pack of jerks trying to do the same to you. It helps to have someone around so you can wingman for each other and joining a corporation is a really good idea.
The combat is intense in small engagements, it's incredibly exhilarating in fleet fights, and it's boring as hell in blobs. Losing a fight means your ship is gone and people are desperately trying to lock on to your pilot pod. If you can't get away I hope your clone is up to date. It took me a month of playing to get the skills and resources required to build my first battleship. Losing it was traumatic.
You can mine asteroids for resources but npc missions are decent fun or you can roam through asteroid belts looking for npc pirates to fight. The most amazing thing though is the crafting and market system. I built a space station in a system where there was nothing but asteroid belts and it's still there, a place for people to dock for a while or call home.
EVE is a huge time investment though. Skill progression is based on real time so flying bigger and badder ships takes progressively longer to get to. If you are looking to make money there are thousands of ways to earn Isk ($$) in game but the big bucks are going to involve farming whatever you find works well or getting involved in 0.0 sectors, the wild west of EVE. Most of the 0.0 regions are controlled by large, well organized, militaristic alliances. It is a pretty daunting game to get into but like I said, if you fly around with a friend and try out a few of the things you can do in EVE you will definitely have fun. It is a cutthroat game though and it's not for everyone.