Wireless router range

Only between machines within your home. Nothing helpful for the internet. Apple routers don't have modems built in so you will need to get an external docsis modem.

 

higher bandwidth usually means 5GHz, which has less range than 2.4.
2.4 is better at getting through things like walls and furniture.

if your house is large or has thick walls, you might be better off with multiple base stations. Your devices will switch as you move around the house.
with multiple base stations, you'll also be much better off with wired ethernet between them.
wireless extension will lead to a drop in bandwidth, as the remote unit has to transmit to both the main base and your computer. For internet this might not be noticeable, but for file transfers it will be. or if you're gaming, you probably don't want this either.

for remote base stations, the new airport express is pretty nice, dual band, not too big, and a decent price.
if you decide to use a wireless connection between the main and remote bases, you will need to go all apple. With a wired connection, you can mix and match.

i've got a Linksys E4200, in the same room, i get 450mb/s (actual transfer speed about 33 MB/s), one room away (but there's a closet, so 2 walls), connection drops to 250-300 (about 22 MB/s).

 

Not only your router is gonna be in the play here. Range of router is 1, but your device also needs to communicate back. A big range of your router is only good for receiving.

If the device you're using has low power on sending, you can forget about the whole thing. This together with the laws regarding emitting energy are the reason why almost all wifi products are the same on this point. Some have worse, some have better range, but the products you're talking about are virtually the same on that point.