There are some pretty deep threads on this on the forums, so you can find more info in those.
The short answer is any BS or T3 cruiser will work depending on how you want to run them and what your skills are. Lots of people (including me) love the Rattlesnake, but if you hate drones, perhaps look at a Machariel if you want something for blitzing. Bhargests are also popular.
If you want to dive into some debates on the pros and cons, check this:
meta schmeta - go with what you like over meta, I say. Much would depend on various factors such as what weapons you prefer, are you wanting to do full-clear or blitz of missions, is the fastest mission completion time possible important to you, is ship/fit price critical, etc.
There isn’t really a “best” ship , only what tool you prefer to a job.
If you are starting back, Raven are a good start before going into navy/pirate battleships, Apocalypse too.
The Raven can be fitted with a Large micro jump drive and cruise missiles for example, so you don’t need a beast of a tank.
It depends on who you are running the missions for really. Whilst you could get a decent mileage out with something like a Raven Navy Issue / Golem, you could also do better with a ship that gets a bonus to the damage that the enemy that you are shooting is weak to.
Decide how you want to run your missions: blitz,full bounty, full clear (full bounty and full salvage)
Decide where you want to base your L4 mission hub out of (region determines main pirate faction, but around 50% will be other factions)
Decide on how much recurring cost for ammo and availability to obtain (market or self manufactured) you want to spend. Drones will reduce this number.
If blitzing, Mach is hard to beat.
If full bounty, almost any high dps BS will work, pluses if able to switch damage type. Rattlesnake would fit in here.
If full clear, Marauders are king. Go Golem/Vargur for damage type options if only buying one. I rotate all 4 depending on opponets. The Marauders large cargo hold combined with an MTU and salvage drones makes full clears a straight forward task; earns up to 20M+ isk per larger missions in salvage alone.
Bottom line, however, is take any ship that allows you to be having fun when you run a mission. Try a speed and maneuvering type, undergun or underton your ship for more challenge, etc. Don’t burn out on missions, since CCP has told us several times that they aren’t planning on making any new ones any time soon. Welcome back!
As said above, depends how you want to run your missions and also more importantly, what side content do you want to do. Running L4s will get you bored and you will want to go do something else to break it up.
Battleships are good for full clears on the big missions. Most missions however are not the big ones, they’re mid size. The small and big missions are about equal and when you average it all out cruisers greatly outperform battleships.
Battleships can do epic arcs completely solo, at least some of them, in particular MJD + cruise missile based. Rest have a much harder time or can’t do them solo. Cruisers for the most part can not solo epic arcs.
Cruisers allow you to do more side content.
You can take your cruiser into Abyss. Can’t take battleship. This one is huge. If you run L4s, you will want to do Abyss, so why not do it in a ship that can do both ?
You can train up to T3C and do some serious explo. Can’t do that in battleship.
You can run DED sites in Gila all day long, a lot of DED sites you can’t enter in a T3C or battleship.
Battleships are far superior over cruisers in AFKing / Botting. Doing L4s in a cruiser requires active gameplay. You have to watch your speed, switch targets priority (in case of webs, cap drains etc), while in a heavy tanked battleship not so, unless you are doing either epic arcs or Angel Extravaganza bonus room, or equivalent content.
You can welp cheap ass cruisers in PvP all day long, just pick a T1 hull with a half decent T2 fit on it, you’ll be using same skills / training only switch hull and fit and you’re good to go, not so in battleships due to costs and to an extent, speed. Get LS escalations ? Go in a T1, you won’t break clear speed records but will still do fine and if you get popped its no biggie.
That all said, best PvE ships are Gila, Rattlesnake, Loki, Tengu, Ravens / Navy Scorp, Machariel There are some situations where other ships will outshine these in specific cases, but overall and on average these are really the best and most flexible.
Weapon system wise, missiles and drones beat the hell out of turrets, exception being the Machariel, but then it has the limitations listed above. Sure there are other turret ships that can do it, but its like driving a car without power steering or power breaks. Just because you can does not mean you should.