The dude I ended up thru'ing the AT with did it with This $35 Tent. The thing survived 2200 miles!
ninja edit
It's got some pretty significant bad reviews on Amazon.
http://www.amazon.com/Texsport-Saguaro-Bivy-Shelter-Tent/dp/B000IU11MS
You are probably not going to find anything significantly less expensive, but you may be better off going with something higher quality that you will not need to repair/replace as often.
For lightweight camping, I'm a big fan of Hammock Camping - Often lighter weight than a single person tent.
I stay drier off the ground, and It's a LOT more comfortable than a foam pad on the hard ground - A good night's sleep makes camping a LOT better for me. :)
You aren't going to find a good complete setup in that price range.
However Hammocks are not as universal, because they aren't great in cold weather(Without significant investment in an underquilt), or in areas without a lot of trees.