But AWS could be really complex. It`s not easy if you want a "professional" environment.
If you have 0 Linux knowledge i would even not deploy my live app on a digital ocean server.
If you want a managed hosting, go http://www.fortrabbit.com/laravel-hosting
And Forge isnt a hosting provider. Forge just setup the complete environment for you.
If you have Linux knowledge Linode would also be an option.
And if you go for AWS you have lots of additional option like external databases, instances, automaticly scale your instance, loadbalancer etc.
And you have 1 micro instance for free.
But as i said, AWS can be really complex :)
And if you want to have much RAM & CPU i would go for a dedicated server.
All the cloudserver companies like Digitalocean, Linode, AWS are really expensive if you need much hardware ressources.