2005 Mac Mini, can this connect this wirelessly to my home network as an iTunes server

I have acquired a 2005 Mac Mini which appears to need direct cable connection to my router to access the internet. Is there a way around this that I can modify to access my home network wirelessly so I can use this as a stable location for my itunes library rather than my macbook pro. The Mac mini is located in a room upstairs but my router is situated in the lounge alongside my Apple TV. I want to try and get the mac mini to be the storage location for itunes that my apple tv will use.

Would the addition of an airport express or the like be a solution or am I barking up the wrong tree. Due to the age, is it likely that the mac mini can be used as a mini desktop only rather than as a file server?

Any help with this would be greatly appreciated, as you have probably gathered, I am an apple novice