One of the wholly unnecessary reasons that schemes are regarded with such fear by so many mathematicians in other fields is that three, largely orthogonal, generalizations are made simultaneously.
Considering a "variety" to be Spec or Proj of a domain finitely generated over an algebraically closed field, the generalizations are basically
Allowing nilpotents in the ring
Gluing affine schemes together
Working over a base ring that isn't an algebraically closed field (or even a field at all).
For many years I got by with only #1. More recently I've been interested in #1 + #3. Presumably someday I'll care about #2, but not yet. Anyway I think it's crazy to give the impression that the three are a package deal that one must buy all of simultaneously, rather than in much easier installments.
I think it could be useful to explain which subfield of mathematics, or which important example, motivates which of #1,#2,#3 is really a necessary generalization.