See that your computer is a desktop there is no advantage to go wireless unless you want to move the unit to difference room or you have a laptop that you want to use around the house
There is also disadvantage in the transfer of data via hard wire computer will transfer data at 100Mbps wireless will transfer at 54Mbps
If you need to access the router to change the setting it is strongly recommended by All router suppliers that you use a physically connected cable to the Router via a Ethernet RJ45 cable for router setup.
My personal view leave the desktop hard wired and only go wireless if there is a laptop or a other desktop in house that need to access your local network to share files, printer, and the internet.
Note: - Wireless is just a way to remove the running of Ethernet cable allover the house or building. Personal I would always go with a wired system
There is also security question with going wireless, as your system data can be access thought the wireless system
If you are not going to use the wireless system for now disable it in the router until required
Check this site will help you to understand how to set up a home wireless system