I'm in the camp that the upgrading the ethernet connection will not help or have anything to do with sound quality. Just make sure it's Cat5e or Cat 6 and that the cable is well terminated and you will be fine.
The best solution, if you can swing it, is to run an ethernet drop from where you modem/router is to where you streamer/DAC is. If you are in a single-story house, you can probably run the cable through the attic and down the walls to ports on both sides. Nice and clean.