For what it's worth, having the Asurans able to construct Atlantis city ships (presumably at a huge cost) and the Tau'ri not having access to one is the right way to go. So good choices there.
Unless you're going for a re-enactment of the series, there is no reason why the Tau'ri should be able to build Atlantis. Starting with one would a HUGE balance issue and problematic. Plus, to do it properly you would have to have the ship virutally useless at the start and somehow have a way to "find" ZPMs, which in itself presents several issues given the way Sins works (having them as planet artifacts gives them to any/every player who holds the planet, and wouldn't behave the way a "found" ZPM would. Secondly, you can't truely customize the artifact to each race the way I'd think you'd want to). There is only one really feasible way that I know of in Sins to limit a ship to only one the whole game, and that's to give them something at the start of the game that is not buildable/replaceable. If you just give them an Atlantis you have major balance issues. You could give them another ship/structure that can spawn an Atlantis at some point but that doesn't really work with the way the Tau'ri should have access to Atlantis either.
If you want an imperfect suggestion for how to do it, I would seed your galaxy with ZPM artifacts on planets. You then have give the Tau'ri starting planet/homeworld a hidden ability that can spawn a "functional" Atlantis once you have an "Activate Atlantis" research finished. The Activate Atlantis research would require 3 ZPM artifacts before being researchable (research is the only thing that can require artifacts as a pre-requisite). Once you research it, the ability would spawn an Atlantis in the gravity well. There is no way to make an ability a one-fire type thing, but you could possibly put an insanely long cooldown timer (like 9999999s I'm not sure if this is doable or would cause problems for the engine) on the ability to fudge it. It's not perfect, but it might be close enough to suit you. Incidentally, you could also use the ZPM artifacts to allow the Wraith to spawn a Super Hive in a similar fashion. I have no idea what you'd do for the Asurans though... preferably I'd allow them to expand their fleet a little bit extra or allow an extra few levels of antimatter research maybe but neither makes total sense for them.
As to the suggestions about using textures from my mod in this mod... The person who posted that it wouldn't work right is correct. They wouldn't on SGI's custom models. Frankly, my textures are mostly quick and dirty affairs as well and need several issues fixed with them too. I have, however, long ago told EO he is welcome to borrow what he would like from my mod and that would include any models if he chose but most of them were donated or borrowed from other creators in the first place so there is the whole approval/credit thing to consider.
-dolynick