What should I do about missed prayers if I was unable to perform them on time because I was away from home, and should I prioritize the obligatory prayers over the Sunnah prayers, or vice versa, when time is limited?

Whoever has missed prayers to make up must hasten to make them up as much as possible at any time. It is not enough to make up only one missed prayer with each current prayer. Rather, one must make up what does not cause hardship to one's body or wealth. If one does not know how many prayers are due, then one must repeat prayers until certain that one's obligation has been fulfilled.

As for supererogatory prayers (nafl) before making up missed prayers, some scholars have deemed them absolutely forbidden if the missed prayers were without a valid excuse, with some excepting the Fajr sunnah (ratibah) and Witr prayers. Others have permitted restricted supererogatory prayers, such as all the regular sunnah prayers (rawatib) and Witr. It is more preferable to hasten to make up the missed prayers and not engage in supererogatory prayers, especially if the missed prayers were missed without an excuse.