This foremost depends on your ‘tier’ of ISP package – or how good your internet is.
DSL (“High-Speed” typically 1-10mbps or so) or Broadband (“Extreme” typically 15mbps or greater)?
Current Mbps rates (download and upload)? [
Test using LAN connection from your ISP Modem]
How many LAN devices do you have that support Gigabit [will be 10/100/1000 in network specs]?
How many wireless devices do you have – or think you will have in the next few years?
Do you have or do you think you will get any wireless devices that support 802.11n | 5Ghz?
[e.g. 'Smart' phones]
Do you stream media [playing video files from one device to view on another]?
If you do stream media, is it Standard or High-Definition content?
Do you game online [PC and/or Consoles]? {Flash games don’t count}
Do you run a home/small business? [Better security features may be necessary]
Approximately how many feet in all directions from its proposed location do you need WiFi to reach?
Do you live in a multistory house [you may require a “repeater” or additional Router]?
What’s your budget range?
All of that will ultimately help narrow down what caliber of Router you will most benefit from.
In addition, you should make a list of all of your network devices/models and look up their network specifications. Write them all down to reference. That will greatly help you make a better informed decision of what you actually will require in a Router, in addition to the aforementioned.
Anyway.
Basically, if you have say a maximum of five or so wireless devices and of the older 802.11g/draft-n variety (and no need of 5Ghz band – like for ‘smart’ phones), don’t stream media or game online, and don’t need better security (WPA2-PSK is the minimum recommended today) then any basic single-band Router with a high end-user rating (far more important than marketing mumbo jumbo) would do.
If, however, you do have a lot of wireless devices (especially if used simultaneously) and any of them support 5Ghz or 802.11n that you wish to benefit from, stream media (particularly in HD) or game online, and/or have a large area to cover, then you’re going to want to be looking at a higher caliber Dual-Band Router (lot more Bandwidth too... and unfortunately a higher price range for it).
You may also find the following article helpful:
How to Buy a Wireless Router | PCMag.com
Special note: A patched Router’s performance can be significantly hindered by an older/outdated ISP Modem. Many ISPs don’t automatically issue their newer Modems that support better speed and bandwidth even if they have bumped up your service tier. So you will need to call them and request that if yours is older than a couple of years (there shouldn’t be a charge; check TOS/contract to ensure they're not attempting to rip you off). In example, I had Verizon’s older Rev. E for a year when I really should have had their Rev. I. after they had bumped up our ‘tier’ from 50/15 to 75/75. The performance practically doubled after the swap.