There are a number of factors which govern the choice of choosing a good hosting service. Some of the major factors are :

1. Price
2. Webspace
3. Technical Requirements
4. Hosting Quality
   

If you are looking for a free hosting service with maximum flexibility. Then I would recommend you to sign up for

www.l4rge.com

If you wish to choose from a range of available free hosting services. Check out this page.

http://www.free-webhosts.com/

All the service which offer free hosting also offer paid services. So you can start-up with a free service and then once the idea clicks move on to the paid service on the same server.

If you are after Name and Quality. You can go for big brand names like Yahoo. It offers paid hosting for reasonable price and almost 100% uptime.

If you still need anyhelp on how to host a new website, try the Hubpage Host-a-New-Website.