I used to shoot some architecture.
You want a lens that is 15mm or wider, to get those really stunning photos, especially the indoor ones.
Architecture demands the extremes. With a wide angle lens, the "scope" of a photo is what draws you in. Foreground elements (say, a spiral stairway) get bloated out of proportion, so you need to be aware of that, but you can use it.
(random example:
http://1.bp.blogspot.com/_2fdwS3Y1V...1600/Absolutely_Stunning_Architecture+_04.jpg)
You can get stunning outdoor shots with very long lenses (300mm or longer) as well, but that's only from long distance. The perspective compression of these long shots can make a building really feel like part of something bigger.
(random example:
http://www.flickr.com/photos/davidyuweb/7692829846/)
You CAN get along with a crop-factor body like The Ti3 or D3200, but you will need to invest in one of the 8mm or 10mm wide angle lenses.
Be aware that these lenses will not work properly on a full-frame camera, if you do end up upgrading later.
The widest full-frame lens (non-fisheye) is the Sigma 12-24mm. So 12mm is as wide as you can go on full-frame. Sigma also makes a 8-16mm for crop bodies (both Nikon and Canon), so you can find an 8mm lens (equivalent 13mm) on a crop sensor.
Both of these lenses are over $1000 for the lens alone.
The widest full-frame lens that I've ever seen for sale at a super cheap price (under $500) is Sigma's old 15-30 lens. That will work on a full-frame body, but is a bit hard to find and has some nasty distortion (which is easy to fix in Lightroom using the built-in profiles). Sometimes you'll find one of the old 10mm or 11mm crop-sensor zoom lenses from Canon, Sigma or Tamron on the market too. Those can be good values, but I don't know exact prices.
I just found this one online. Good deal...
http://www.amazon.com/Tamron-10-24mm.../dp/B001G7PIBC
You can get an 18mm lens on your crop-frame body for super cheap, but the effective 24mm is just blah boring for architecture. Again, wider is better, shoot for under 15mm, although the 10mm above (equivalent 16mm) should cut it on a crop-sensor body.
good luck!
Edit: PS, avoid having people in your shots with the 15mm and wider lenses. They get really weird looking at that range unless they're at a distance and near the center of the frame.