Capships for Casuals or Beginners

[Lemon]

For PvE and Zoi
go for Ranseour in Omicron Tau

Tanky, easy to manouver unlike the zoner blob
And great missions, often with allies. And you can choose between easy and hard ones (crayter spawns carriers and dreads on relatively low level missions, BGH has cruisers even on high level ones)
With a PoB that buys your spoils at nice bonus prices so you get extra money unlike in delta.

Add to that a massive ZoI people keep whining about nonstop that lets you go on trips and you have an easy pick. This is my Go-to ship for farming cruiser missions and I have 5 heavy battle ships now including the neph.

For your last point and if you want missions and easy frequent PvP , arbiter's your choice, you might have 3 techs to choose from (legion, Civ AND liberty as the ID it getting merged with separatists) and has decent mission systems. Although in PvP it's flak and secondaries are very hard to use because of it's ridiculous lenght + placements