Choosing a Home Router

It's remarkable how many options there are, and how unorganized the information is.
Let's jump to the bottom line, and then get back to details and spec:

As of 2016 my recommendations:
If your modem speed is 50-100MBs, buy VDSL2, 802.11n (or better) and 10/100Mbs or better

If your modem speed is better, or if you pass large files inside the nwetwork, make sure your wireless and wire speeds match it. 

And for the gory details:

Wireless speed (this is total, if you have 2 clients, they will share bandwidth)
2.4Ghz/5Ghz need to be supported on your laptop/phone.  Most support 2.4Ghz and the newer (>2014) also support 5GHz, which is much less crowded.
In my neighborhood, using the first caps me at 6-10MBs, due to interfeences, and the later can achieve 30MBs.

 

802.11 ac -(both 2.4 and 5Ghz in parallel)  - >> 2GBs

802.11 n - (both 2.4 and 5Ghz in parallel) max of 150MB (1 antena) to 450MB(3 antenas)

802.11 a - (only 5GHz) - 54MB (lots of time less)
802.11 g - (only 2.4GHZ)  max 54MB  (sometimes more, lots of time less)

802.11 b - 11MB 

Wire speed

10/100/1000 Mbs - means supports network cards of 10Mbs and of 100Mbs and of 1000Mbs.

10/100 Mbps - only supports up to 100Mbps
I suggest, As of 2016, to buy at least 10/100Mbs, 

Modem speed
Do you have cable-type or DSL type?  see below for DSL type only:
VDSL, VDSL2   : max of 100MB download and upload (usually lower with distance)
ADSL2+ : max of 24MB download and 3.3 upload.

ADSL     : slower