Upgrade from Dynamics CRM 2011 (partner-hosted) to Dynamics 365

We want to upgrade one of our clients system from Dynamics CRM 2011 (partner-hosted) to Dynamics 365 Online. One approach is to upgrade our system in the following order:

Dynamics CRM 2011 to Dynamics CRM 2013
Dynamics CRM 2013 to Dynamics CRM 2015
Dynamics CRM 2015 to Dynamics CRM 2016
Dynamics CRM 2016 to Dynamics 365.

Are there any third party tools or firms which can help us upgrage our system to Dynamics 365 database in the manner suggested above?
Suppose we get our database upgraded to Dynamics CRM 365, will Microsoft help us to use this database and provide us with a running Dynamics 365 online instance?
Please suggest.

Any other better approach is also welcome.