If you are just interested in the quantum mechanics of SUSY (rather than its quantum field theory), you should read the comprehensive (though now 20 years old and no longer fully up to date) survey article
F. Cooper, A. Khare, U. Sukhatme,
Supersymmetry and quantum mechanics,
Physics Reports 251 (1995), 267-385.
The math is straightforward analysis of ODEs, so no special safeguards are needed.