which bread goes stale the fastest, rye, white, or wheat? And why?

This is going to be a difficult project, since "stale" is not a
scientific term. It seems to me that you'll need to come up with some
objective way to measure "staleness" before proceeding.

One way of measuring 'staleness' might be to measure moisture loss (or
moisture content before and after).

Owain

Rye breads are know to stay fresh longer than wheat breads because it
absorbs more moisture. (even though it contains less gluten than wheat
breads)
Then white bread stay fresh longer than whole wheat bread because it
contains more gluten. gluten helps having the bread rise higher and
have a better texture, moister, that stay fresh longer.
So called 'bread flour' are flour which contain some additives, like gluten.
You can also add gluten to your homemade bread to help preserving them.

If, by "stale," you simply mean "dry," it won't be difficult to
conduct your experiments. You can simply weigh the before-and-after
pieces of bread, with the assumption that any weight that is lost was
moisture.

However, to me, "stale" implies more than dryness. There is a slight
rancidity, a taste change, in stale breads. That isn't going to be
easy to quantify.

Bonhomme gives some facts that the school project can maybe verify.
And now I know why bread wrappers proudly proclaim: Gluten enriched.
Living in the land of Brot, I know that bread isn't just bread, even
the squooshy (?) loafs in the States. The more airspace in the bread,
the faster it can dry, and I doubt that that will be the same for the
three types of bread used in the project.  And what about other
additives that influence this?

I think the school project will  - hopefully -  lead to a discussion
of all this, and more, but remain inconclusive, but that's fine  -
it's a learning experience, and we may have expanded the discussion.
I also agree with Pinkfreud (always hard not to) about the smell, but
that is very subjective.  A pipesmoker like me probably won't notice
till the spores of fungus appear, and still eat it anyway.  I
understand one shouldn't but
- qoutes of the day:  
Paracelsus:  "Everything is poisonous, it's the dose ..."
Nietzsche:  Was uns nicht tötet, macht uns stärker."  :)