Modems with built-in routers are terrible.
1. switch out the POS you have now with a modem only. It’s worth the drive. Do it now. I’ll wait…
2. Get a $60-130 Linksys or Netgear router (preferably Linksys).
3. ????
4. Profit
You don’t have to do any port forwarding for gaming if you have a decent router and you should NEVER be kicked completely off the internet unless it’s down in your area.