It's a good bit of kit.
In theory you can attach a hard drive but in practice I believe this does not work too well as the hardware is not up to running the internal server software. It is much better to run the server software (Logitech Media Server or LMS) externally and have the Touch connect to that.
You could try it out on any PC initially, though you will probably want to find a more permanent solution at some point. Basically if you want the system to be on and accessible pretty much at all times, you will need to have LMS running somewhere. Some people use an old laptop and it is possible to run LMS on certain NAS drives.
However, it is becoming increasingly common for people to run LMS on Raspberry Pis, which are more than powerful enough in their current versions, while drawing sufficiently low current not to worry about leaving on all day. (In case it sounds a bit scary, setting up LMS on a Pi is really simple - people have already done the complicated bits, so it's just a case of downloading software and copying it onto an SD card - there is plenty of help out there.)