I am wired. It looks like a coax cable goes into the router and regular cat6 cables are going out to the PCs.
My router says MI424WR, it appears to be Actiontec. It's black with silver.
As for the upgrade, I took the advice below and canceled the upgrade order until I can do more research. I don't know why (naive? lol), but I just assumed getting faster service or paying more might make it better.. the whole 'get what you pay for' thing maybe, I don't know. I'll chalk it up to naivety/general stupidity for now.