Alice Rogers Supermanifolds is a rigorous introduction to supermanifolds in the geometric and algebraic approaches with the emphasis on the geometric. She also discusses applications to physics such as the Wess-Zumino model, the basic example of a 4d N=1 supersymmetric theory as well as BV quantisation of gauge theories which is naturally formulated using supermanifolds. She also discusses applications to maths, for example super Lie groups & algebras. Obviously these are important to physics too, for example, the Wess-Zumino model is constructed using the super-Poincare group.
Gijs Tuynmams, Supermanifolds and Supergroups is more of a reference. He rigorously develops manifold theory over a graded commutative ring which specialises to the real, complex and super manifolds. There's much less motivation and applications here than in Roger's text. There are various definitions of super manifolds, not all equivalent, and he focuses on the de Witt's $H^\infty$ supermanifolds on the geometric approach and the Kostant-Leites sheaf-theretic on the algebraic approach. Roger's also develops the former, but focuses on a broader class she calls de Witt $G^\infty$ supersmooth functions.
I also found Cattaneo & Schatz's Introduction to Supergeometry useful. They not only discuss supermanifolds but also graded manifolds, an even analogue of supermanifolds of which examples are Poisson manifolds and Courant algebroids.
I'd say of these three, Roger's is the most elementary in the sense you are asking for. Certainly I found the text approachable even when I knew next to nothing about rigorous differential geometry.