You would actually only apply to Engineering.
You can apply Early Admission (but that is binding but way to go if VT is your first choice). Otherwise apply Early Action (do not wait for Regular decision as there won’t be a lot of spots left then).
If you look at the active thread here at top for EA (Early Action) you will see lots of posts of SAT/GPA and those getting into Engineering.
With you having a 4.4 currently overall you should have a good shot at engineering. Just get a good SAT and good math grades and your in good shape.