There is no such thing, you may be mislead or even nieve, but nothing is unlimited. There is a limit. It may be high but the host you are with has to work within the capacity of their servers. There are hosts who appearon the scene, offer unlimited all the way and then dissappear a few months later. Well that's why, they can't maintain what they set out to offer.
So what should I go for.
The best way to start out uis with a free host like fast-host which offers a good 300mb of disk space. If you are starting out with a website to show your friends your photos or to start a blog this is way way more than you will need. In fact that is a lot of space for a website. The also offer 10 GIGS of bandwidth, Now that is more again than you will need for most sites. If you are going higher than that you really want to be looking at paid hosting!
A free domain dame is always good. Fast-host again offer that from their home page and on your sites first home page when you set up the account. This is easy to set up and if you have any problems there is a live chat support featurre
What about paid hosting!
This is for sure an option if you have had a site for a while or require more services like accessing your database from home. (You can access your database in free accounts through a web browser). There is better service for paid accounts, like ssl security certificates and own IP which is needed for some professional options.
Fast-host will be offering their own paid hosting from Feb 2011 and will be offering special offers to anyone who signs up to free hosting before the end of on January 2011.
This is a great deal, You can even let the administrators know what you would like to see in the free offer either by visiting the site and chatting with the admin team or leaving a message if nthey are not there. You can alsoTWEET your suggestions to the admin team at Twitter: @fasthost_tweet