Website linking

I have purchased the domain name at godaddy. Few things to be done.
1. How to have the real site without go daddy name and publish it.
2. Need to build the site and find out the cheapest platform to do it and link it.
3. Need to build the site and publish it. Link the email name which is bought and connect to gmail so easy to check mails, if any on that.
This is an initial work to start with as of now.