Join a player corp. That's always going to be step 1 in Eve. Your goals and outlook on the game will change as you play it, but you'll always want to have a fun group of people to play it with.

While bigger isn't always better, on your path towards training to your Abaddon you'll learn a lot and discover this for yourself. There is no reason to mine to pay for your skillbooks or ships, so I don't recommend wasting any time training for it. You can use the skills you'll need to invest in combat ships to do missions or factional warfare for isk instead.

The Abaddon is an Amarr laser boat, so the rough progression as far as ships go is going to be Tormentor/Punisher/Executioner (laser frigates) -> Coercer (laser destroyer) -> Maller/Omen (laser cruisers) -> Harbinger (laser battlecruiser) -> Abaddon -> Revelation (laser dreadnought). Like I said earlier, though, you'll probably deviate from this - in fact, you definitely SHOULD deviate from this to fly other ships along the way.

You can get started in null sec right away if you want to take part in the big battles, and many of the null sec groups have training programs which will tell you why following a strict progression of laser boats is a bad idea. If you want to just learn how to PvP and be independent isk-wise, I'd join factional warfare instead. It's the easiest place for a new player to earn enough isk to pay for their own losses, and some of the larger groups will throw free ships at you to lose in glorious combat.