The Rebbe's guidance on what to look for in a shidduch centers on essentials rather than externals:
The foundation is yiras Shamayim and daily observance of Torah and mitzvos. This is the first and foremost requirement, and one should never compromise on it (IK 9447, 9489, 10786). A home built on Torah values brings true happiness, more than outward appearance or what society thinks (IK 1001, 5957, 9041).
Focus on what truly matters and don't look for perfection. Perfection belongs only to Hashem; searching for it in another person leads away from happiness. When the inner qualities come first, the external concerns often resolve on their own (IK 3430, 4895, 5930, 5946). Look at good middos and sincerity, and don't be put off by status differences (IK 9468, 4338).
Judge a person by who they are now. Negative reports about someone's past need not be a concern when their present conduct follows the Torah; teshuvah changes a person (IK 4200).
Don't set Chassidus study as a precondition. Sincere yiras Shamayim will lead to Chassidic practice over time (IK 3479, 5535).