One of the joys of Eve is that the four factions have ships and weapons systems that feel different to fly. There’s not “best” ship, but rather “What do I prefer to fly in certain circumstances?”.
I’m largely an Amarrian pilot, but do fly the ships of other races.
Amarrian ships are typically capacitor demanding, armour tanked and using frequency crystals (faction for combat against other players, T1 for missions as they are not consumed). An Armour tank has the advantage in taking less capacitor to repair than a shield tank does to boost as well as more options for configuration with a greater range of modules.
The general challenge for a lot of players is that to go down an Amarrian path is to focus on Armour skills, you will need Energy Turret skills (Amarrian specific), and good capacitor skills. It all starts to feel a long way from a lot of player’s initial training around shields and either drones or missiles - that may be why a lot of people fly “non-Amarrian” ships: because they’ve not trained into Amarrian ships.
Amarr includes some of the good Drone ships, although they have less role in a fleet - the Arbitrator is a cracking drone based crusier, but it’s main role is a support ship - e-war for a fleet for example rather than pure DPS. Likewise the Dragoon and Armageddon are drone ships with Cap Warfare bonuses (I knew someone who used a cap-war fitted Dragoon in faction warfare to great effect)
So, pure Amarrian options:
Faction Warfare: I know the Slicer and the Punisher are successful, as is the Coercer.
You can gank in a Coercer. But Ganking is hardly an honourable pastime for God’s ships.
Mission Running: Level 3 - Harbinger, Level 4 - Apocalyse. Navy versions if you like really easy.
The Anathema is a good exploration ship and a quarter the price of an Astero (which you’ve already trained the same skills for)
PvP Doctrines: The Harbinger fleet backed by Guardians is a common enough sight. Oracles for demolition work. Abaddons with Guardians for battleship work.
I don’t do Incursions but I’m not surprised Paladins are used there.
Amarrian ships are perfectly fine, but most people don’t prioritise the skills needed for them.
I did and I’m very happy flying them.