A good character to start off with is Kayle. She is only 450 IP so you can get her after a couple games if she isn't free. She is a support/carry who can heal and make people invulnerable but also does a lot of damage with reckoning and righteous fury. She is rather forgiving because of the invulnerability and good escape.
Ashe is a great starting character. It gives you good practice with Skillshots from her ult, and helps you get the gist of CC, as you can potentially permanently slow someone with ice arrows.
She's also one of the cheapest characters in the store, so it wont take long to unlock her.