Which should a person prioritize; settling his debt or providing sustenance for his family?
Alhamdulillah, praise and gratitude to Allah SWT for His countless blessings for us all. Praise and salutations to our beloved Prophet Muhammad PBUH, his family, companions, and all those who follow his footsteps until the Final day.
Sustenance lexically means providing, which means financially providing for his family. While in syarak, it means a provision in terms of food, clothing, shelter and others. It is named Nafaqah for it is spent for this need. 
In al-Sunnah, there is a hadith narrated from Mu’awiyah al-Qusyairi RA, where he asked the Prophet PBUH: “O Messenger of Allah, what is the rights of a wife on one of us of which is obligated for her husband?” Rasullullah PBUH replied:
أن تُطْعِمَها إذا طَعِمتَ ، وتَكْسوها إذا اكتسَيتَ ، أوِ اكتسَبتَ ، ولا تضربِ الوَجهَ ، ولا تُقَبِّح ، ولا تَهْجُرْ إلَّا في البَيتِ
“That you should give her food when you eat, clothe her when you clothe yourself, do not strike her on the face, do not revile her or separate yourself from her except in the house.” 
Syeikh Wahbah al-Zuhaili said the majority of scholars stated the obligatory sustenance to be given to a wife are the following seven matters which are, food, groceries, clothing, house, personal hygiene appliances, houseware, assistant for his wife is his wife usually has an assistant. 
Scholars have agreed (ijma’) that the husband is obligated to provide sustenance for his wife. Furthermore, this still applies even if his wife works and has her own income and wealth. The responsibility of the family’s sustenance is on the husband. This is based on the statement of Allah SWT:
وَٱلۡوَٰلِدَٰتُ يُرۡضِعۡنَ أَوۡلَٰدَهُنَّ حَوۡلَيۡنِ كَامِلَيۡنِۖ لِمَنۡ أَرَادَ أَن يُتِمَّ ٱلرَّضَاعَةَۚ وَعَلَى ٱلۡمَوۡلُودِ لَهُۥ رِزۡقُهُنَّ وَكِسۡوَتُهُنَّ بِٱلۡمَعۡرُوفِۚ
“Mothers may breastfeed their children two complete years for whoever wishes to complete the nursing [period]. Upon the father is the mothers’ provision and their clothing according to what is acceptable.” 
Ibn Kathir stated in his commentary that it is obligatory for the father to provide in terms of appropriate clothing which is customarily accepted in the country without being wasteful or burdensome. It is in accordance with his (the father) financial capability in times of ease and moderate as well as what he is used to. 
In the issue of sustenance, it should be properly understood. The reason is sustenance is a crucial element in marriage and included under the responsibility of the husband over his wife under his care.
In the discussion of sustenance, jurists have divided it into three groups of husbands, the wealthy, average and low income. If the husband is poor then it is sufficient for him to provide the basic sustenance, such as one mudd of rice as well as basic dishes accompanying the rice according to the local custom. Next, the basic clothing for his wife to wear following the local custom when she is at home or outside, covering her aurah. Then, provide a place to live according to his capability, without it being conditioned that he owns the house, it is enough if he’s only able to rent it. If the poor husband fulfils all these basic needs, then the wife doesn’t have a right to demand a fasakh. 
One should realize that marriage comes with responsibilities for both the husband and wife. However, believe that Allah SWT will never burden or even oppress a husband. Believe that everything that is sanctioned by Allah SWT has great wisdoms behind them. This is as clearly stated by Allah SWT in the Quran:
لِيُنفِقْ ذُو سَعَةٍ مِّن سَعَتِهِ ۖ وَمَن قُدِرَ عَلَيْهِ رِزْقُهُ فَلْيُنفِقْ مِمَّا آتَاهُ اللَّـهُ ۚ لَا يُكَلِّفُ اللَّـهُ نَفْسًا إِلَّا مَا آتَاهَا ۚ سَيَجْعَلُ اللَّـهُ بَعْدَ عُسْرٍ يُسْرًا
“Let a man of wealth spend from his wealth, and he whose provision is restricted – let him spend from what Allah has given him. Allah does not charge a soul except [according to] what He has given it. Allah will bring about, after hardship, ease.” 
In regards to debt, lexically it is any form of liability (burden) in the future which is the responsibility of a person in the form of cash or others.
In al-Fiqh al-Manhaji, it is stated: According to jurists, the terminology is used to describe a handover of ownership of a certain item to another on the condition the other person returns it without any additions. 
Indeed, Islam emphasizes the concept of debt through the statement of Allah SWT:
يَا أَيُّهَا الَّذِينَ آمَنُوا إِذَا تَدَايَنتُم بِدَيْنٍ إِلَىٰ أَجَلٍ مُّسَمًّى فَاكْتُبُوهُ ۚ
“O you who have believed, when you contract a debt for a specified term, write it down.” 
Other than teaching the concept of debt in Islam, it also emphasizes the commandment to settle one’s debt. This is clear as what happened during the time of the Messenger PBUH according to a hadith narrated by Salmah bin al-Akwa’:
أَنَّ النَّبِيَّ صلى الله عليه وسلم أُتِيَ بِجَنَازَةٍ، لِيُصَلِّيَ عَلَيْهَا، فَقَالَ ” هَلْ عَلَيْهِ مِنْ دَيْنٍ ”. قَالُوا لاَ. فَصَلَّى عَلَيْهِ، ثُمَّ أُتِيَ بِجَنَازَةٍ أُخْرَى، فَقَالَ ” هَلْ عَلَيْهِ مَنْ دَيْنٍ ”. قَالُوا نَعَمْ. قَالَ ” صَلُّوا عَلَى صَاحِبِكُمْ ”. قَالَ أَبُو قَتَادَةَ عَلَىَّ دَيْنُهُ يَا رَسُولَ اللَّهِ. فَصَلَّى عَلَيْهِ.
A dead person was brought to the Prophet (ﷺ) so that he might lead the funeral prayer for him. He asked, “Is he in debt?” When the people replied in the negative, he led the funeral prayer. Another dead person was brought and he asked, “Is he in debt?” They said, “Yes.” He (refused to lead the prayer and) said, “Lead the prayer of your friend.” 
Such are the teachings brought by the Messenger PBUH who not only came to teach people about worships and maintaining the relationship with Allah SWT, but it also upholds the muamalat relationship amongst people as something that shod never be neglected. Other than the incident the Prophet PBUH refused to lead a funeral prayer and just let another companion leads it, the matter of debt is also emphasized in a narration from Abu Hurairah RA, where Rasullullah PBUH said:
نَفْسُ اَلْمُؤْمِنِ مُعَلَّقَةٌ بِدَيْنِهِ, حَتَّى يُقْضَى عَنْهُ
“A believer‘s soul remains suspended according to his debt until it is settled or paid off on his behalf.” 
Such is the grave effect of those who didn’t settle their debts, indirectly the above hadiths ruled that not settling one’s debt is prohibited.
According to the above arguments and evidences, sustenance is an obligation of a husband as we’ve explained. Hence, in this situation, the husband is obligated to provide sustenance according to the basic minimum sustenance stated above.
We’d also like to conclude that debt and sustenance are two responsibilities that should be fulfilled. However, if the questioner is in an exigent situation, then Islam offer a solution through the zakat system where its recipients include those who are in debt.
The reason is debt is divided into two, the debt that should be settled immediately and debt of which its payment can be delayed or postponed. Imam al-Nawawi said: If he still has some debts that he should settle immediately, when he is financially incapable of doing so, then the creditor reserves a right to stop him from travelling. Consequently, if he is poor and doesn’t have what is claimed from him. At this moment, it is permissible for him to travel without permission. Likewise, if the debt is a delayed form of payment, then it is permissible for him to travel before settling it. However, it is sunnah for him not to travel except he has appointed a proxy that can settle his debt during his absence. 
Thus, we’d also like to advise those who are involved in debt to learn the techniques of financial management. This is important in managing and prioritizing what is essential when one is financially incapable, such as the basic sustenance that he should fulfil for his wife.
Hence, it is important to understand the fiqh aulawiyyat properly. Considering the importance of financial management and matters related to basic expenses as well as for settling a debt that may need to be paid at the same time, however, each should be fulfilled at least the minimum fulfilling each of their rights. At the time a calmness and a correct financial management plan can ease our lives’ burdens who are trapped in the above-presented issue.
We end by presenting a supplication in a sunnah that we can practise in settling our debt and easing our lives’ burdens. This is stated in a hadith narrated from Abu Said al-Khudri RA, he said:
One day the Messenger of Allah (ﷺ) entered the mosque. He saw there a man from the Ansar called Abu Umamah. He said: What is the matter that I am seeing you sitting in the mosque when there is no time of prayer? He said: I am entangled in cares and debts, Messenger of Allah. He replied: Shall I not teach you words by which, when you say them, Allah will remove your care, and settle your debt? He said: Why not, Messenger of Allah?
He said: Say in the morning and evening:
اللَّهُمَّ إِنِّي أَعُوذُ بِكَ مِنْ الْهَمِّ وَالْحَزَنِ وَأَعُوذُ بِكَ مِنْ الْعَجْزِ وَالْكَسَلِ وَأَعُوذُ بِكَ مِنْ الْجُبْنِ وَالْبُخْلِ وَأَعُوذُ بِكَ مِنْ غَلَبَةِ الدَّيْنِ وَقَهْرِ الرِّجَالِ
“O Allah, I seek refuge in Thee from care and grief, I seek refuge in Thee from incapacity and slackness, I seek refuge in Thee from cowardice and niggardliness, and I seek in Thee from being overcome by debt and being put in subjection by men.”
Abu Umamah RA said: “When I did that Allah removed my care and settled my debt.” 
May Allah grant us taufiq and guidance for all the Muslim ummah in understanding and practising His shariah. Amin.