The use of querer in the preterite, in general (not only when followed by the subjunctive) is a lot less common than querer in the Imperfect tense (quería). When we use quise, quisiste, quiso... we interpret this "wanted" as a desire/intention that takes place during a defined time period, or it could also be interpreted as a desire/intention that has just started. For example:
Al acabar el bachillerato, Laura quiso estudiar medicina, pero sus padres la convencieron para que estudiara biología.
(When she finished the sixth form, Laura wanted/had the intention to study Medicine but her parents persuaded her to study Biology.)
As per the use of subjunctive after quiso que, the tense that is normally used here is the Imperfect subjunctive. For example:
Los padres de Laura quisieron que ella estudiara biología, en vez de medicina.
Laura's parents wanted her to study Biology, not Medicine.
Here, this "quisieron que" is taken as a desire that started at some defined time. (when she finished sixth form)
Un saludo cordial