Router Recommendations?
 

So I need a new router. I haven't bought one in years so I have no idea what I need. I have a NAS that I will often stream movies/tv from. Other than that there might be one other person downloading. Don't need too much range as its only about 800sqft.

At this stage, get one with 802.11AC. They have come down significantly in price and the boost in speed and range is well worth it. This plus the fact it's more future proof; unless you plan to wait until 802.11AD comes out.

I have an Apple Time Capsule AC that works amazingly for me. Very easy to setup and the speed is awesome (around 240mbps when copying files between computers on LAN. And I have no problem playing games while wife/in-laws are streaming tv shows/talking on facetime. If you have Apple systems, get this.

On Windows side, I heard many great things about Asus routers. AC68 or 87 particularly. Might want to look at that.

The correct answer to your question depends on your situation. Everyone's answer will will be different.
For me I connect to my router which is 20 feet away and thru 1 floor and 2 walls. 5Ghz will barely do the job, so I use 2.4GHz, which has more range. Wireless AC only works on 5GHz, so it would be useless for me. I like having gigabit ethernet. I recommend something in the Asus lineup. For me a RT-N56U would be nice. I think it might be good for you too. Since you are dealing with 800ft2, you probably don't need anything high end. You can save some money.

AC56U if you need USB 3.0 (probably not since you have a NAS) and excellent community support
if you just want Merlin custom firmware and dont have any AC clients, then I'd go with the N56U
since you live in an apt you dont need the range of the N66/AC66/AC68/87...interference is a more import factor once set up.