How can a young man choose between two girls who are equal in religiosity, beauty, and lineage, after performing Istikhara and supplication without finding a decisive answer, and what is the correct course of action in this situation, especially given the parents' current disapproval of marriage?

If two girls are similar in good qualities, consult those who are knowledgeable about their circumstances, then perform the Istikhara prayer, and ask Allah for facilitation and success. If you are able to bear the expenses of marriage, try to convince your parents. If they are not convinced and you are in urgent need of marriage, then proceed with it and strive to gain their رضا (رضا translates to contentment/pleasure). If you are not able, then fear Allah and be patient, and work on what helps you maintain chastity, such as fasting and lowering your gaze.