I'm sure someone from Texas Tech will come around eventually to give you some specific information but
generally speaking you want to avoid the following:
1. Cleavage
2. Mini skirts/dresses
3. Anything super tight
4. "Clubwear"
5. Anything extremely loud in general
Now I would think the difference between a casual sundress and church attire would be that a casual sundress would be appropriate to wear for anything from hanging out with friends to a casual luncheon (as long as it follows the aforementioned guidelines...so not something you'd throw on over your bathing suit at the beach for instance). Church wear would likely involve more coverage and be more conservative in general.
As for strapless, as long as it doesn't involve cleavage I would be surprised if it were a no-no (at least on the casual sundress day), but a Texas Tech student/alum should be the resource for that answer.

I would say something like this would be appropriate for the "church attire" category. (Provided recruitment is around the time school starts, though, if you chose something with a similar print as it is spring-summer appropriate.) Basically your thighs are covered, it's not backless, and it isn't strappy or tight. Though as katydid said some people might think those shoulders are too bare, but it's easy to find a dress that is sleeveless but still covers the shoulders or one that has cap sleeves. (I'm assuming rush will be held while it's still hot outside here).

This would be an example of an appropriate casual sundress...it is not super short, does not show cleavage, and has substantial straps. Steer away from anything that will be very low cut, has itty bitty straps, is very short, or is sheer (it's just too difficult to be positive nothing will show through).

Though if you are busty I would choose something more similar to this style wise, as you're less likely to end up with accidental cleavage. For a casual sundress it wouldn't necessarily have to be THIS long or this "nice", but different body types require different styles to remain conservative.

Lastly if strapless is ok, this would be an example of a safe way to do it. Covers the girls, isn't super short or tight.