3800 square feet might be too much for any single router. Multi-story house with basement? Eeeek. Might be tough, if not impossible.
If you're willing to tweak, I would look at the
Routerboard stuff, but otherwise I would be looking at the Netgear WNDR4500 or Asus RT-N66U. Not sure on the Linksys E4200 V2 (especially if you want aftermarket firmware, at least not yet at this point in time) yet, although it looks solid otherwise.
Smallnetbuilder.com also has excellent reviews, including range.
If budget is a concern-- or you find that there's no way you can cover 3800 square feet of interior walls and whatnot with a single AP, two cheaper ones might work. The older Netgear WNDR3700 v1 or v2, WNDR3800, WNDR4000, Asus RT-N16U or RT-N56U, or the Linksys E4200 original (aka v1) would all work, and I believe you can grab some of these for as low as $80 refurb'ed...
FWIW, I am find that about 2000 square feet on the same floor with interior walls is doable with any of the routers listed, but as you've got double that... I dunno...