I will now outline the pro's and con's of hosting on a free or dedicated server.

Free joomla hosting.

1) Ok it's free, big bonus.
2) You will be provided with a sub domain like username.hostingcompany.com rather than aspecific domain name like joomladesigns.co.uk. A free sub domain does not give a good first impression to your clients, visitors
3) Free web hosting offers limited space between 50 / 100 MB. If you plan to expand your web site as it becomespopular this could be a bad move using a free web host.
4) Free web hosts are also know to be unreliable, not good if you want a stable environment for your new joomla site.
5) Free hosts offer lower bandwidth so if your site get's really busy then it could become unavailable due to bandwidth restrictions
6) You also get less functionality than the paid joomla hosting companies. Some free hosting companies may not support php, mysql or Zlib in order to run joomla!
7) Free hosts need to generate an income, in order to do this many free host's include banner ad's on your website again now good if you want to make an impression with your customers.

Please note free hosting is great if you want to created a HTML based site for testing or wish to test out your new joomla site but remember it has limitations..