While you're building and testing your Twilio code, you can run it on your local machine with ngrok, but once you're ready to go live, you'll need a real web hosting provider (or your own server). Here are some recommendations:
Heroku (https://www.heroku.com): This is owned by the enterprise software powerhouse Salesforce, and specializes in making it easy to deploy and scale applications with no server expertise. It's free to start with and supports essentially every language and framework you can imagine. However, it quickly gets expensive as you scale.
DigitalOcean (https://www.digitalocean.com): This is the fastest growing hosting provider in history, providing cheap and endlessly configurable cloud servers from $5 per month. It's an excellent platform but requires a fair bit of knowledge to configure your own server.
Fused (http://www.fused.com): This specializes in hosting for small- and medium-sized businesses with a special focus on great customer support. You can...