EVE New Citizens Q&A

If you want to PvP as your main activity, I'd advise getting L3 (or I suppose L4) missions rolling as your primary source of income and exploration sites as your secondary.

That way if you're running short on cash you can go spend half an hour at your mission hub and get 4 or 5 fitted ships worth of isk without wasting too much of your time, and when you're out looking for 1v1 in low-sec you can smack some RAD sites around to pass the time.

Mining's reliable and can be pretty profitable but the time investment can make it hard to do that when you're doing casual-schedule PvP unless you're into something really specific (like mining in a bait ship with a stealth buddy to jump people that come for you).