https://www.amazon.com/dp/B0111MRLES/ref=dp_cerb_1
this is a docis 3.0 modem. its rated for 100 mbps and its around $40 so i would think it would work. just be aware that its not really future proofed (if you are to upgrade to something higher in the future.)
this is a really cheap router i found off of amazon with mostly good reviews. i dont know how well it works, but if you want, you can test your luck. its also wireless n, so it isn't that bad.