1st order of business is to contact a salesrep, as you will need licences to deploy to a private server (Windows or Unix) OR a licensed slot to one of the Mendix Cloudservers.....
I also suggest that you read some of the documentation on "how to deploy..."
For the second part of your question..
1) o a private server you will have to give the application a web-adres to work from and you will need to have your ISP manage the DNS related stuff that goes with that 2) when you deploy on the cloud the adress will be along the way of [your application].mendixcloud.nl or .comand Just ask your ISP to set up a C-name record in DSN to give it a more appropriate "public" name