The model number gives you that...N means it's 802.11n. Routers that support ac will always include that in the model name...like AC1900, or whatever.
Your network adapter's not gonna do any better than your router can provide...but the good news is, the router has more speed than your ISP. That's your #1 limiting factor. So all you need is an N600 adapter. And IMO going PCIe won't matter; this is not a taxing load. But you do want to get dual-band. If you have to go with, say, an N900 adapter to get the dual-band, it's a little excess capacity, but c'est la vie.
Actually...that router's probably 300 Mbps at 2.4 GHz, and 300 Mpbs at 5 GHz. So if you want to, you can go with an N300 at 2.4 GHz.
Finally, if you want to look ahead, you could spend a bit more and get something like an AC1900 adapter. That'll usually give something like 450 Mbps at 2.4 GHz, and 1450 Mbps at 5 GHz. This is serious overkill *for now* but if your situation changes, this will still fit the bill.