Hello,
I am not sure if this is the type of answer/information you are looking for but I figured I would tell you what I use. Before I jump into that I would guess that the stuttering / stammering is due to one of two things, network speed (shouldn't matter if you have a modern wifi setup or a wired connection) or more likely your TV's CPU is unable to handle the transcoding of the media smoothly. I have a VERY large media collection with several TB of music & movies in various formats. For streaming, backup, and a "central repository" for all of it I built a small home media server. I use a HP Microserver (was 150 USD a couple years ago on sale) with several drives (1 TB drives 50 USD) running a free Linux OS (Debian). It is connected to my main PC via Gigabit ethernet BUT ALL of the streaming I do daily is done via a wireless N network to a old Western Digital media player &/or TV. I use SAMBA so all of the drives on the Microserver are usable by the windows machines, streaming devices, tablets, etc etc. I know a lot of people steer away from Linux as they fear it will be difficult to setup & administer but I assure you there are HUNDREDS of easy to follow guides for Media Servers that can walk you through the setup start to finish. Also if you are on a budget don't feel you need to use a prebuilt or new machine for your media server as almost any old PC (hard drive space is the only real requirement) will do the job. I have built several media servers for friends/family who have seen my setup using old stripped out PC's or Ras Pi's with external Drives hooked to them for free or little investment. Something you may want to try is experiment playing different file types on your existing setup. For example if you find that .avi video files play well but .mp4's dont you may want to use one of the many free video conversion programs to transcode or slightly lower quality on your media before streaming.
Hope this helps some and that you are up and watching your content soon!!