Advice for Dummies
I see no need for another router if it's all co-located. Some other tips:
1. It helps to have an ethernet cable just in case you lose wifi and need a quick way to get to the modem for any reason. If the modem and computer are co-located as you say, I'd recommend using an ethernet cable over wifi, because it's just basically simpler and you get max bandwidth out of it, no matter what.
2. 5GHz vs. 2.4GHz wifi: If you are located in the same room as the modem and must use wifi, it's best to use the 5GHz wifi channel if possible. It's generally faster than the 2.4GHz channel. However, it's possible your computer doesn't support 5GHz so I'll give you the best settings for both.3. 5GHz wifi settings: Check to see if your computer supports 802.11ac over 802.11n or 802.11g.
If it's able to do so, this should allow you to expand the bandwidth of a single wifi channel from 20 to up to 80MHz, which also makes it faster. Then you can check how the modem is set by going to it's Advanced Setup/Wireless page (you may have to log in using the router password). The settings you want are under 5Ghz, where it should be:
Wireless Mode: 11a/n/acBandwidth: 20/40/80MHz
Leave "Channel" alone and "Extension Channel" should get filled in by itself.
Click "Save Settings" if you've changed anything and the modem should restart with those settings.4. 2.4GHz wifi settings: Not as good, but if youre limited only to 2GHz (the section just above 5GHz), the settings for that should be similarly:
Wireless Mode: 11b/g/n
Bandwidth: 20/40MHz
Leave "Channel" alone and "Extension Channel" should get filled in by itself.
Click "Save Settings" if you've changed anything and the modem should restart with those settings.