For a while I did a lot of mining and lowsec ratting with LegoEggo.
After that we headed to nullsec and set up camp, where I trained nearly all the skills I needed for PvP in my harbinger. I did some PvP, then nullsec mining and whatnot. I don't play anymore though. My sub ran out a few months ago and I really don't have much time for EvE anymore. I probably won't re-activate it until around September, if then.
I'd say one of the most important things you need to do in EvE is get into a nice, friendly, active corp who aren't very uptight about things. It really helps a lot. PvP is also a very fun thing to do. When you're in a fight with someone and it comes close - especially your first few times - you can damn near have a heart attack. It's funny how exhilarating a game can be when you know everything is on the line.
Also it might help to set some long term and short term goals and work towards them by mining or whatever while waiting for skills and such.
Try and make some friends to mine with. I've actually had a lot of fun with large groups of people while mining for hours. Just chatting the entire time. A lot of the time the groups were made up of people from multiple other corps.
