In faction warfare, you typically generate income through PVE missions but recent changes mean loyalty points are awarded for PVP kills. Player corporations may also offer a ship replacement program and other assistance for new players. FW corps also tend to place more emphasis on role-play. Amarr FW corporations I know of are:
Societas Imperialis Sceptri Coronaeque (SFRIM)
P.I.E. (Praetoria Imperialis Excubitoris)
Have a chat with their recruiters.
If you think you might prefer Nullsec fleet PVP check out https://www.bravecollective.com/ currently involved in a major war so should be lots of opportunity to shoot stuff!