Whether you agree with this or not, PvP in EVE is a lot of fun. PvP is essentially what the entire game is based around and if you've never given it a try, I suggest trying to get into it somehow. If you can keep the cost of your ships down, there really is no "grind" to pay for ships. A single level 4 mission can give out up to 30 million isk, which is equivalent to losing 20-30 fully insured tech 1 cruisers with tech 1 fittings or 4-5 with tech 2 fittings.

Faction Warfare is particularly good for getting into PvP because it's mostly small gang warfare with small ships. Disposable frigate fleets and destroyer gangs are a common sight.