AppleTV/Roku are useless for this, only the WDTV Live fits the bill.
But your bigger problem is the router and wireless, the file serving capabilities on routers tend not to be very fast and wireless itself is another bottleneck, it might be okay but it depends on your media and how good your wifi is. Browsing network shares over wireless adds a speed penalty but if the router has a UPnP/DLNA server turn it on and access that via the WDTV Live for improved performance.
You could also use a Slingbox as long as you have an IR reliever on your server. Using the remote codes you could browse the files and play then as long as you have some sort of output from the server to the sling. A sling 500 will accept HDMI input. If you get a sling 350 just get an HDMI to component converter and make sure it is powered.
This way you could watch them around your house and away from home as well. Usable on tablets, phones (app costs money) and laptops or desktops (free). Stream adjusts for bandwidth but around the house on the same network I get perfect HD quality.