as for ships directly here’s a breakdown of what is avaliable and cheap for recent players:
-Amarr -> Punisher & Tormentor (Executioner and/or Magnate could be alternatives)
-Gallente -> Tristan & Incursus (Atron is good too, i think, not sure on Imicus)
-Caldari -> Merlin & Kestrel (Condor suffers an specific bonus to a damage type, Heron is capable of even doing PvP)
-Minmatar -> Rifter & Breacher (Slasher can be good, Probe may be capable too)
-Outer Ring Excavations -> Venture (yes, mining is also a PvE activity)
all the destroyers of each empire are fine but you have to simulate them and choose the one you like in addition to that theres
-Society of Conscious Thought -> Sunesis (its the little brother for the Gnosis, a versatile destroyer that can fit any weapon and tank, it may be quite expensive tho).
-Amarr -> Maller, Omen, Arbitrator (its special because of the drone bonus)
-Gallente -> Thorax, Vexor (Celestis doesnt have a weapon bonus like the Arbitrator so its more of personal choice if you want a 3rd option)
-Caldari -> Moa, Caracal ( same as with Gallente, the Blackbird in theory can serve as 3rd combat option)
-Minmatar -> Rupture, Stabber (Bellicose is the missile option but its also an EWAR boat so take that in account)
-Society of Conscious Thought -> Gnosis (the most versatile battlecruiser in the game, its price can be hard to cover depending on the season because of its limited avalaibility)
much like with cruisers each empire has at least 1 dedicated to each doctrine. there’s also the Attack Battlecruisers (Oracle, Naga, Talos and Tornado) which use Battleship sized weapons but in turn are more nimble in terms of defense. those arent really used in PvE or at least in missions, perhaps they have a niche in other PvE combat activities that i dont know of.
-Society of Conscious Thought -> Praxis ( the new kid on the block in the battleship neighborhood, it may be quite expensive due to being a recent addition to the game)
most of the battleships on each empire are capable of running PvE. except for the Caldari Scorpion, because it has been deemed an EWAR battleship, you can still fit it for tank and bring weapons but it may have low DPS for its size.
i’d like to include hauelrs in this list because there’s also courier missions that you can run with them. the first lvl can be done in any Exploration Frigate. but from L2 to up you need an industrial.
any industrial from each of the empires can run them as long as you investigate which is the maximum cargo size of each mission lvl and fit the ship to do it along with proper tanking and speed mods.
you may have notice i put SoCT in the lists but not other factions, its mostly because those are the typical swiss army ships that are recommended for missions or other stuff. so i deemed it worth to mention.
Navy and Pirate ships are more of a long term investment so i wouldnt recommend rushing to them right away. first try to master what you can fly atm.
and yes, there’s a “Mastery” system for ships in the game if you’re new and dont know. you can check it in the info of the ship. it may be a good indicator in order to see how to advance with them.