cat5e, yes, https://www.amazon.com/gp/product/B00DES2FQW/
My opinion, even though people say you won't exceed it's speed, it to get in to 802.11ac as soon as you can. It's a huge improvement over 11n, not just in speed. Asus makes a decent AC1200 router (http://www.amazon.com/ASUS-Dual-Band-Wireless-Router-RT-AC56U/dp/B00DES2FQW). Netgear makes some decent AC1600 units (http://www.amazon.com/NETGEAR-AC1600-Wi-Fi-Gigabit-Router/dp/B00BR3ZYIW).
Don't get so hung up on the 1200 v 1600 v 1750 v 1900. Most of it is marketing and fud on inflating the practical use of the higher speeds on the 2.4Ghz band. It's most important to focus on the 5Ghz and making sure it's a 3stream 11ac 5Ghz radio (99% of the time you will want 20Mhz 2.4Ghz because the spectrum is so crowded).
IMHO main thing to focus on is 3-stream 11ac 5Ghz radio and the best CPU you can afford. smallnetbuilder is a reliable source. For consumer-grade devices, I've had good luck with Asus and Netgear. Your mileage may vary and there will be TONS of opinions on this. Up to you if you want to pay more for the faster AC units. The AC1450 and AC1200 Netgear units are within your price range.