Leo says David will want an 802.11n dual-band router. Linksys is the cheaper brand, and it's not free of problems. David will want to make sure not to get one with "WPS" security. This is the "one-button-push" security, and it's very insecure. It also can't be disabled on most Linksys routers, so stay away from those. The best router in Leo's opinion is the Apple Airport Extreme, but it's much more expensive, nearly twice as much as the others. If price is a concern, he recommends D-Link.
The reason there are "dual-band" routers is because the 2.4Ghz band that Wi-Fi had always been on, is now getting crowded. The reason Wi-Fi was on this band is because it was unregulated and set aside by the FCC so anyone could use it. As a result, a lot of other things are on that same band as well, causing issues with Wi-Fi.
So newer routers support both 2.4Ghz and 5Ghz. 5Ghz is less crowded, but it also doesn't reach as far, and doesn't travel through walls as well. If there's no congestion at all, the 2.4Ghz band will work better in a home. However, if there's a lot of congestion, the 5Ghz band is preferable. Most routers will give him the choice, and he could try both to see what works best. It's always a good idea now to get a router that will handle both bands just in case the 2.4Ghz band becomes crowded.
There are also Wi-Fi standards. The first was 802.11, then b, g, a, and then n. 802.11n is now the standard and the one that he should get, but there is a new standard coming called ac. There are a couple of companies making "pre-ratification" ac Wi-Fi access points. The problem with ac, however, is that all devices on the network has to support this. AC has some great features, including the ability to aim itself at the devices receiving the signal.