"New router? Apple Airport? I'm looking for an easy solution that will work..."
For the easiest solution that works, get an Apple Airport Extreme base station.
I have Uverse, and the residential gateway that they provide only provides "g" wireless speeds, not the faster "n".
The very first thing I did -- with the Uverse installer guy still present -- was connect my Airport Extreme via ethernet, and TURN OFF the wireless broadcasting on the Uverse residential gateway. I have never used the wireless in the residential gateway.
It worked from the get-go, no problems.
IMPORTANT:
When you set up the AE base station, you want to choose the option to disable NAT, and instead run it in "bridged mode" (so you don't end up with NAT on both the residential gateway _and_ the AE).
You do this by launching Airport Utility, then go to the "network" panel, and in the "Router Mode" popup, select "Off (Bridge Mode)".
If you don't mind buying an Apple refurbished product, you can go to
http://www.refurb.me
and pick up a refurb Airport Extreme Base Station for $125.
Try this link (may not work)
http://www.refurb.me/us/browse/#!apple-refurb-store-Mac-Accessories-refurbished-Mid-2011-id-3818
Note: I just checked and it said this is the June 2011 product -- if you want newer, you'll have to "buy new".
It might be worth it to pick up the latest Airport Extreme (the tall one), to "be ready" for the future...