This is a very complex question in reality
The simplistic answer is given above.
Mainly due to ship size and raw fire power it is clearly.
Frigate <-- Destroyer <-- Cruiser <-- Battlecruiser <-- Battleship <-- Capital ship.
T2 ships are specialised as RoKera & aragaer points out. HACs and Combat Recons pull well above their weight in combat, and certain configs of Strategic cruisers are pretty much unstopable if operating as a group.
All high tier ships aside, as you are talking about a new toon, if you are asking more about efficiency, ie which ship should I aim to be in for fleets, the Battlecruiser is by far the most well rounded of the combat ships.
Let me explain, think like a stack of cards where frigates are numbers, Dessy's Jacks, Cruisers are Queens, Battlecruisers Kings and Battleships Aces.
By this definition Aces are high and the battleship is King or rather Ace.
Destroyers beat Frigates.
Cruisers beat Destroyers & Frigates.
Battlecruisers beat cruisers & Destroyers & if set up correctly Frigates.
Battleships beat Battlecruisers.
But, Frigates can't kill battleships, but a good frigate pilot is pretty unkillable by a battleship. They get in close, orbit. shoot it's drones and keep it pointed.
Fleet is then like a game of poker, to get a Royal flush you need all the cards !
Battlecruisers offer the best balance between destructive firepower, maneouverability and engageability, without the high price and vulnerability to small ships...
Of the Battlecruisers my favourites, Hurricane is the most Flexible, Drake is best PVE and Brutix does most DPS at the cost of survivability, Harbinger is also an excellent combat vessel and can vary it's range well.
However don't go right for battlecruisers because to get the most out of them you will need good supporting skills in shield or armour tanking maneuvoring warp and cap management and T2 guns.
Key point is all ships are useful in combat and any fleet needs the small as well as the big, month old characters are just as useful as Pointing tackle as the heavy hitters, they all have jobs to perform and the ones that work like an orchestra in symphony play the best melody's.
For your interest Caps perform specific functions.
Dreadnaught - DPS (Smallest Cap, main use in POS bashing and anti Capital warfare)
Carrier - Support (capacitor transfer and repair, usually spider tank with other Carriers) these are usually present only in CAP fights or for PVE assigning fighters (Which can warp) to ships running plexes.
Super Capitals
Super Carrier.... Like a carrier only bigger, can also carry bombers when CCP fixes them.
Titan, Beheemoths of the skys...... Massive DPS, pretty much unkillable without another titan or vastly outnumbered. Also can be usef to jump ships around without a stargate.
