While not personally familiar with your new modem, I think the basic steps you want to do are as follows:
1) log in to your router via a web browser. The user manual for your router will describe how to do this.
2) assign a static local area network IP address to your Slingbox, so that this LAN IP address assigned by your router to your Slingbox will always remain the same, in case your router is rebooted due to power loss or other reasons. The user manual for your router will describe how to do this, and should require the MAC ID for your Slingbox, which is printed on its shipping box and also on a sticker on the bottom of the Slingbox.
3) Program your router to forward port 5001, for both the TCP and the UDP protocols, to the static LAN IP address that you assigned in Step 2.
4) Reboot the router and reboot the Slingbox, and you should be good to go.
Glad to hear that it is working out for you. I think the basic steps to get a Slingbox to work on a network are straightforward enough, but it seems like every router uses different procedures (and sometimes even different terminology) to do it that it generates lots of confusion among users. Just like power supplies for laptops, I suppose. I think I own 6 laptop computers, and every one of them has a different type of AC charger and pin-size for the plug-in to the computer. All incompatible with each other, and likely to fry the laptop if I were to attempt a workaround.
I have not programmed any Quality of Service parameters on my routers for any of my devices or forwarded ports. But then, I don't use my router or network for any "high-bandwidth-required" activities (such as video Skype?) other than my Slingbox, so I have no "competition" among devices wanting to use the bandwidth simultaneously. So I've not experienced any data saturation or other problems that might cause the Slingbox images to freeze or stutter where a QOS assignment might be helpful. So I would suggest that you just try your Slingbox without QOS programming, and then only experiment with QOS if you find a less than satisfactory viewing experience.