Level 75
Develop offline. Hosting, there are many different ones, D.O. AWS many use shared hosting, some now use Vapor, etc. Depends on app, client, and other things.
Like asking what make of car do you drive. You won't get one answer, you will get many.
Edit: Here is a decent discussion on hosting, was before Vapor:
https://laracasts.com/discuss/channels/tips/hosting-on-shared-server-best-practice
It includes Digital Ocean also.