NQT: If you're ambivalent about killing people how are you going to find scu- oh wait, wrong forum.
Impressions from a relative newbie:
Basically, do all the missions for the career agents first. If you don't buy stuff from the market, you should end up with a few million ISK and a good handful of ships. I don't *think* anything was too hard in those missions.
The tutorial missions that require you to lose a ship give you one to lose first. Make sure you make that ship your active one before undocking. Also, if you buy the maximum level of insurance for it before you blow it up as part of the mission, you'll make extra money.
Don't shop for skillbooks until you've done all the career missions. You might get it for free from the tutorial/career missions. When you do shop for skillbooks, look for the seller who has (I think) 555 to sell with a duration way over 90 days. Those are NPC sellers, and you can get all of the basic, NPC provided skillbooks at that same station. These will likely cost you an arm and a leg more if you buy them elsewhere.
1.0 - 0.5 = highsec = You *can* get killed, but your killer will be killed by NPC police very shortly thereafter. And vice versa. Usually you won't get attacked in highsec unless you're carrying cargo around worth billions of ISK.
0.4 - 0.1 = lowsec = You have a significantly higher chance of getting killed, and your killer will be accosted by the turrets around the warp gates.
0.0 = nullsec = Anything goes. Anything.
After you finish the career missions, look up the "Sisters of EVE" mission arc. That's what I did, and you shouldn't have much of a problem until you have to hunt down Dagan.