I did this last year and it takes several "hops" to get from 2011 to 2016/365.
I highly recommend a conversation with your vendor/partner first.
My next recommendation is to run the Custom Code Validation and Legacy Feature Check utilities. You can find a good write up on them here blogs.msdn.microsoft.com/.../legacy-feature-check-and-custom-code-validation-tool-demos-for-upgrade-to-crm-2013
These tools will give you a heads up on issues with bad endpoints, js code, etc., that should be noted and corrected as you move forward.
Next step would be contacting vendors of any custom solutions loaded in your organization for updated solution files.
I used separate servers for each version as we moved forward. I did not perform in place upgrades and don't know if that would work for you.
The first jump is from 2011 to 2013 SP1, the lowest version which will allow the jump to 2015.
From 2013 SP1 you can jump to 2015 and from there to 2016(8.0).
We ran through these upgrades several times in test environments before making final run in Live environment, you should do the same with user acceptance testing also. Just because the upgrade worked does NOT mean the parts as a whole still function the same way.
We did no customization apart from loading updated vendor solutions in the entire run from 2011 to 2016.
Once you get to 2016 you will most likely want/need to merge your current forms up to the new forms model. This is a pretty straightforward process, but does require you to lay the fields out on the form again. Initially these are all added to the bottom of the new form. I found this a good place to involve power users and other staff for direction on new form layout.
We have since upgraded to 8.1. I cannot give you information on 365 as we have not gone there even in test yet.
Hope this gives you some direction to begin putting together a plan for your company. Let me know if I can assist further.