To be able to edit the PHP, do FTP and shell, you will need to host your own installation of the wordpress.org software on an independent web host. What you are talking about doing cannot be done here. There are limitations on what can be done here due to the structure of this platform. WordPress.com is a multi-user platform which means we all share the same underlying theme and WordPress core files. With around 30 million blogs here, security is a high concern, so that means we cannot add plugins or any other code such as javascript since any bad code added by one person could bring down a lot of sites here.
For more on the differences between WordPress.com and WordPress.org, take a look here: http://en.support.wordpress.com/com-vs-org/ .
Most web hosts offer installation scripts for the WordPress software, so it can be reasonably painless getting the basics up and running.
You can see here for some recommended web hosting: http://get.wp.com/hosting/ .