This solution prevents duplicates:
q1 = Q(...)
q2 = Q(...)
q3 = Q(...)
qs = (
Model.objects
.filter(q1 | q2 | q3)
.annotate(
search_type_ordering=Case(
When(q1, then=Value(2)),
When(q2, then=Value(1)),
When(q3, then=Value(0)),
default=Value(-1),
output_field=IntegerField(),
)
)
.order_by('-search_type_ordering', ...)
)