My parents have been using Xfinity for a few years now. We currently have wifi in our home, but the connection length and bandwidth is extremely bad. I have a big family, so everyone in the house uses the wifi for gaming, computers, tablets, ect. We currently have the default Arris modem which connects our phone and wifi together. Because of the number of people using the wifi, it cuts off sometimes. Other times it becomes limited, so consoles work but people using their computer aren't able to browse the internet. I was checking my modems home by logging into it and I noticed something that I wanted to ask about. For 1, our current mode is set to 802.11 g/n. The other option is for b/g/n, which I have no idea what it means. I searched google, but it wasn't a clear answer that helped me understand rather I should choose 1 or the other to increase my homes bandwidth. I also wanted to know what would be a good router to support my homes bandwidth? I was suggested Dlink, but for a home with 5+ people using the internet I wanted something that would allow everyone to do what they wanted without our crappy isp's limitations. Another possible solution I thought of is using a router that was given to me to setup for the top level of my home, while using our current Arris modem for the downstairs. Would that be a suitable solution this this issue?
In general, modem routers tend to suck for wireless - they have too many design compromises, and a good router would make all the difference. Product suggestions are off topic for SU, but the wirecutter has a good set of suggestions comprehensible by mere mortals
You don't want bgn mode enabled unless you have devices that need 802.11b - these are older devices mostly. As long as everything can connect under ideal conditions you don't want this. In fact, if possible, I'd use the modem router for G connections only and get a new router set to N only. In general you do not want to enable legacy modes unless you need them specifically
You do want a second router or an access point, and if its a modem ideally one that can be switched to access point mode (alternately switch off DHCP, and connect your Arris Modem Router to a lan port). You could use wireless bridging or some kludge like WDS, but that means you're sharing wireless bandwidth between them. Go wired between routers/APs if you can.
A good router should be able to handle all those clients readily, and be accessible throughout a reasonably sized building. I'd try putting it next to your modem router, setting it as an AP and connecting them and seeing if that makes a difference. If you have range issues, rather than keeling over and dying cause of overuse, consider moving the second router, connecting it to the main AP over ethernet (if you can) or homeplug.
I live in an area with lots of wireless routers, so I tend to use the mobile version of inssider to pick which channel to use - its got a few features the free desktip version dosen't, and in some situations this may help too. If you're using more than one router, it makes sense to put them each in one of the three non overlapping channels (say 1 and 11).