Q:

First rock band ever?

Rock music is a genre of popular music that originated as "rock and roll" in the United States in the 1950s, and developed into a range of different styles in the 1960s and later, particularly in the United Kingdom and the United States.

What is the first band that could be determined as Rock?
I mean the first band that had some different features from the past genres and that determine the passage to this new gerne known as Rock.
I have some ideas, such as The Beatles, Rolling Stones, The Who...
Help me in this deep research!

A:

If we are talking about 'Rock' distinct from 'Rock n' Roll', then it should have these features:

Power chords, or at least aggressive chords on guitar, featuring the minor pentatonic scale
Guitars are distorted (amplifiers)
Driving drums
A guitar solo would be a boon here

A lot of suggestions have been given to the forefathers of the early rock n roll landscape.

The Beatles were a pop band more than anything.  None of their albums featured anything this driving until the White Album
The Dave Clark Five emulated the Beatles sound.  They are, therefore, more pop (or rock n' roll if that offends some) than Rock
The Animals released House of the Rising Sun in early 1964.  Wikipedia identifies this as one of the earliest Folk Rock songs.  This song lacked distorted guitars (the organ was the prominent voice)
Surf Rock started as early as 1961.  The signature guitar sound of Surf Rock lacked distortion (but featured reverb)

This leaves two real contenders:

The Kinks released 'You Really Got Me Now' in 1964
The Who released 'My Generation' in 1965, about a year later

Both of these songs satisfy the conditions above.  Both have distorted guitars and angsty vocals.  Both have guitar solos.
The Kinks, FTW.
EDIT: since there is discussion based on the comment to my first answer, I will put that back up here:
Chuck Berry is the first musician to play a guitar in a Rock fashion.  Whether or not his backing band were all playing what you might consider Rock, none of us might be playing Rock, Hard Rock, Heavy Metal, etc. without Chuck Berry.
You have to mention his name as The Inventor.

