That's a great question. The most popular Messenger bot in the industry, and the one we choose for ourselves and our clients is ManyChat
ManyChat has all the features you'll ever need and you can start with a free account. The Pro version (which includes important features such as admin notifications), starts at only USD$10 per month.
It does take a little time to get used to how it all works, but once you do, it's a very intuitive and easy-to-use service.
One of the features we love about ManyChat is that each of your automated bots is made as a flow chart. This makes it easy to see how the conversation is progressing.
Here's an example of a simple flow chart which schedules a live demo: