Short answer. First priority goes to the surviving spouse or next of kin, or someone they request, if competent and willing. If they are unwilling, incompetent, or neglect to act within thirty days, priority shifts to a principal creditor, and failing that, to whoever the court selects.
What the law says
If no executor is named in the will, or the executor or executors are incompetent, refuse the trust, or fail to give bond, or a person dies intestate, administration shall be granted: (a) To the surviving husband or wife, as the case may be, or next of kin, or both, in the discretion of the court, or to such person as such surviving husband or wife, or next of kin, requests to have appointed, if competent and willing to serve
Rule 78, Section 6 — When and to whom letters of administration granted. Read the full provision →
First priority: the surviving spouse and next of kin
The rule's first preference goes to the surviving husband or wife, as the case may be, or next of kin, or both, in the discretion of the court. It also allows appointment of such person as such surviving husband or wife, or next of kin, requests to have appointed — the family closest to the decedent effectively gets to nominate who administers the estate, so long as that nominee is competent and willing to serve.
Second priority: a principal creditor, after thirty days of inaction
If the spouse, next of kin, or their nominee is incompetent or unwilling, or if they neglect for thirty days after the death of the person to apply for administration or to request that administration be granted to some other person, priority shifts to one or more of the principal creditors, if competent and willing to serve. The thirty-day window gives the family real time to act before this shift happens.
Third priority: whoever the court selects
Only where there is no such creditor competent and willing to serve does the rule fall back to letting the court choose freely: administration may be granted to such other person as the court may select. This is the court's residual authority, used only after the first two tiers of preference have genuinely been exhausted without a suitable candidate.
When this priority order applies at all
This order of priority comes into play if no executor is named in the will, or the executor or executors are incompetent, refuse the trust, or fail to give bond, or a person dies intestate. Whenever administration — rather than executorship under a validly named executor — is what the estate actually needs, this tiered priority is what governs who ultimately gets appointed.