Your notebook streaming over the wireless is the bottleneck but maybe it will work for you but just dont go expecting to play 1080p content over wireless.
What you could do is buy a
cheap network hub/switch for 20 bucks and place it in an easily accessible location so you can plug your laptop into it at any time but also have the media player plugged into it that way you dont have to worry about speed issues. The media player doesn't have to be plugged into your Internet router with its built in hub if its stuck in a particular location.
A NAS is basically a storage device that sits on your network it appears as a computer in your network browser and you can copy files to it, both devices can read these folder shares and play media from them.
A basic NAS like the one I linked doesn't have much in the way of features or upgrade-ability whereas there are high end ones that have lots of features and options.