Which schools within UVA (Arts and Sciences, Architecture, Engineering, Kinesiology, etc.) are the most in-demand and in need of applicants?
UVa publishes data online about the numbers of applicants and admission rates by school. I don’t think any are “in need of” applicants.
Charlie is right. Apply to the school that you feel is the best jumping off point. You can always look into switching to a different school within UVA at the end of your first year if you realize that the fit wasn’t quite right.
If a person is 50-50 undecided between engineering and arts and sciences, it is better to start in engineering. That is because engineering has a more rigid curriculum, and it will be easier to finish in 4 years if you start and finish in engineering. If you later transfer to arts and sciences after the first or second semester, you can still graduate on time with an arts and sciences degree.