What documents to show if I'm a US citizen with no US passport to re-enter the US?

I would recommend that you do contact US Embassy and get issued a passport or a travel document that will let you cross the US border.

There is a site from Department of Homeland Security that shows the necessary documentation to cross the US border for the US citizen, which states:

Air Travel

All U.S. citizens including children must present a passport or other approved travel document when entering the United States by air. U.S. citizens can present a passport, NEXUS card at airports with NEXUS kiosks, U.S. military ID with travel orders, or a U.S. Merchant Mariner Document when on official business.

The land crossings have a slightly different document requirements then Air gateways but even then it's better to have a passport when you cross the border.

In this case what would be the best documents to have for me to gain entry back into the US as a US Citizen without a passport?

If you drop by Canada or Mexico then enter the US by land, you can enter without a passport and without a compulsory trip to secondary, with e.g. a Global Entry card or an Enhanced Driver's License.

https://help.cbp.gov/s/article/Article-3618?language=en_US gives more details:

Land or Sea Travel: U.S. citizens entering the United States by land or sea are required to present a valid WHTI-compliant document, which include:

• U.S. Passports
• U.S. Passport Cards
• Enhanced Driver's Licenses
• Enhanced Tribal Card (ETC)
• Trusted Traveler Cards (Global Entry*, NEXUS, SENTRI, or FAST
• Military Identification Cards (for members of the U.S. armed official maritime business)

* The Global Entry (GE) card is only an ENTRY document and may not be used to enter Canada, Mexico or Adjacent Island.

Military personnel traveling under orders may present photo ID and orders. Family members must present a passport (with the exception of children 15 and younger arriving by land or sea.)

Children: U.S. citizen children ages 15 and under arriving by land or sea from a contiguous territory (Canada or Mexico) may present an original or copy of his or her birth certificate (issued by the Vital Records Department in the state where he or she was born), a Consular Report of Birth Abroad, or a Naturalization Certificate. If the child is a newborn and the actual birth certificate has not arrived from the Vital Records Department, we will accept a Hospital issued birth certificate.

Groups of Children: A U.S. citizen children between the ages of 16-18 arriving by land or sea from contiguous territory and traveling with an adult supervised school group, religious group, social or cultural organization, or sports team, may also present an original or copy of his or her birth certificate, a Consular Report of Birth Abroad, or a Naturalization Certificate.

For more specific information regarding passport documents, please contact the National Passport Information Center.

For documentation requirements regarding cruises, please see our FAQ on "What Documents do I need for Cruises "

FYI: What's the legal consequence of leaving the United States without using one's U.S. passport?

It seems clearly that any person without a passport will be denied to board the plane. HOWEVER, IF A PERSON applies to the us embassy for a temporary pass, then he or she will have no issue. This is just common sense and without reading any law, but emergencies happen and so many considerations may be taken by immigration Agents or airports to facilitate in such emergency situations. I have been in a situation where I witnessed people travel without any document in hand in such circumstances when the reason is known.