I think for all beginners, an essential champion is Jax.

He is incredibly easy to play compared to most champs and will make it easy to learn how the game works.

Explanation of Jax:

He is a melee character with his natural passive being an attack speed increase every time he hits something (Stacks up to six times)

His Q ability is Leap Strike. This allows you to jump to the target (You can use it to jump to an ally which will help you escape if need be) and do an amount of damage if it is an enemy.

The W ability increases the amount of damage done with the next basic attack (Hitting with his staff lantern thing).

Jax's E ability allows you to block incoming basic attacks for a short period of time and reflect damage back to all surrounding enemies based on how many attack you had blocked. It will also stun surrounding enemies when activated again or after it runs out.

The R ability (His ulti) is an increase of Armour and Magic Resistance for a period of time when activated. This ability also comes with a passive however which gives Jax a super-hit every 3 attacks, dealing bonus magic damage.

Advice with Jax:

As your first ability, always get E. This will help you stun an enemy early game to go in for the kill with a teammate as well as enabling you to escape if in danger.

Try to build attack damage first. Due to Jax's passive, if you increase the damage (I would go for a ravenous hydra) then you will still be getting increased attack speed.

Jax's abilities are also increased with ability power so go for an item such as Hextech Gunblade or Trinity Force.

Try Master Yi, he is the nooby champion all the new players use.
He is really easy to use and only cost 450 IP.

Jax is fairly easy, but not completely easy. If you love to be a solo top bruiser you have to develop a mentality along with fundamentals with the game. If you prefer that hyper carry type that just kills everything I recommend ADCs'(Attack damage carry). IMO I just say play someone to fit your play style which you will eventually have after a couple hundred wins. The champs I recommend as a low level:
Mid: Ryze
Jungle: Shyvana(has amazing clearing times and naturally tanky late game)
Support: Soraka(for the basics of being aggressive and passive)
Top: Garen, Master Yi, Darius(Very fun to play), Malphite(helps you learn when to go in and when to become aggressive), Teemo(to kite easily)
ADC: Caitlyn(to kite easily as well), Ezreal(helps you play aggressive at the same time passive due to his E), and Vayne(if you think you're ready to put all the mechanics together)