Most routers/Access Points/Repeaters today support the Wi-FI .11n technology. .11a/b/g technologies are equally acceptable however will result in poorer performance in general. There is also a new technology .11ac that will provide superior performance to 11n.
Before you worry about the specific technology or model for a wireless router make sure you understand what problem you are trying to solve. For example,
-if you are looking for a video streaming solution over Wi-Fi across multiple rooms and walls, you are very likely to need a combination of multiple Access Points.
-if you would like to use the high bandwidth 5GHz Wi-Fi radio, make sure the distance between the router and the Wi-Fi device is not far. In most cases where there is great distance between the router and the Wi-Fi enabled device, 2.4Ghz option yields better performance.
-If you see too many (more than 10) Wi-Fi networks alongside your own home Wi-Fi network, you are likely to have degraded performance. Most of these networks run on 2.4Ghz radio so Switching to 5Ghz radio may help you avoid this congested environment.
-You can also try to change channels of your Wi-Fi radio using the admin console of your Wi-Fi Router.