Heroku

Heroku has flexible pricing - it's free at first and then you pay more as you scale

Heroku's integrated with GitHub enabling one-click deploys

It's awesome for hosting Node and Java projects

Domain Name Registrars

You'll need to have a custom domain

Domain names are actually very inexpensive to register unless you're purchasing them from a current owner of the domain name

I'll assume you've got one from GoDaddy but any Domain Name Registrar will do:

GoDaddy
Dreamhost
Hover
Namecheap
Gandi

Add a Custom Domain to Heroku

Now, go to your registrar's website and find the domain under their domain management tools:

(1) Find CNAME with the entry www
(2a) Then, in the appropriate spot, enter the heroku address.
(2b) (ours is postlib.herokuapp.com)

Then, in Heroku:

(3a) Under Settings find Domain Name and set DNS Target to the custom name
(3b) (ours is www.postlib.com)