In todays world of technology the only two considerations for me would be buried fiber (in a conduit) or wireless.  Due to cost and ease of setup I'd pick wireless.  If installed and configured properly it will be just as stable and fast as any other connection.  Ubiquiti offers great products.  Search the forums and you'll find lots of information. 

FYI.....If you are not sure whether to connect to a router or a "splitter" you need to do some learning before you go to far.  There is no such thing as a splitter in the networking world.  There are hubs (outdated) and switches.  Switches create many from one.