Meteor deployment is always kind of a sore topic, deployment is notably more difficult than expected.
From what I've seen, Galaxy is by far the easiest way to deploy and the project management experience is sweet. Since Galaxy is made for Meteor, the support and ease is kinda expected. However, it can be pricey.
Heroku was mentioned here but I would like to go into a little but more detail. There is some setup that you need to do, but once the initial deploy is ready is should be fairly simple. There are two ways to deal with your DB in Heroku, host is there or add a link for an external DB. Heroku is free up to a point. If on the free tier, the app will not be awake all the time and initial loads take a long time if the app was asleep.
Step by step tutorial for deploying to Heroku here
Well, it is certainly easier to deploy a Node+Express application, but developing in Meteor is way sweeter (in my opinion) and takes care of all the parts of the app. Node+Express means you still have to build a front end, while Meteor is overkill if you don't use all its parts.
Good luck on your search!