Here is a phrase you will be hearing a lot in EVE:
“It depends.”
In general terms, Level 3 and 4 missions require a decent amount of firepower (500+ damage per second, minimum) and either a beefy (ish) tank OR high speed.
Because of this, you should be looking towards Battlecruisers and Battleships.
If you prefer to utilize speed, Cruisers and Battlecruisers.
Bear in mind that as ships get larger, the character skill requirements and technical knowledge needed to use said character skills increase.
This is because larger ships are slower (see: the have trouble dictating range) and have issues with “point defense” (see: NPC frigates become an actual threat)
All that said…
Pretty much any battlecruiser or battleship can run level 3 and 4 missions. Some are more optimal than others, but people do have preferences in terms of what weapons, tactics, and “flavor” (race) they prefer to use.
Unfortunately I can’t give anything more specific without more information.
What kinds of tactics do your prefer?
How much money do you have to work with?
What region of space are your currently operating out of?
Also… relevant topic below. 