Is there a source in Jewish teachings for the importance of maintaining cleanliness and personal hygiene?
In Deuteronomy, the Torah discusses rules that regulate battle encampments. Now, an impromptu temporary battle camp is not a place where you'd expect a high standard of cleanliness. But this is what the Torah says:
And you shall have a designated place outside the camp, so that you can go out there [for use as an outhouse]. And you shall keep a shovel in addition to your weapons; and it shall be, when you sit down outside [to relieve yourself], you shall dig with it, and you shall return and cover your excrement. For the L-rd, your G‑d, goes along in the midst of your camp, to rescue you and to deliver your enemies before you. [Therefore,] your camp shall be holy, so that He should not see anything unseemly among you and would turn away from you.
This standard certainly can be applied to any area wherein we wish to welcome G‑d's presence. And certainly this includes the human body, which is the ultimate Sanctuary for the Divine Presence.
Also of note is the last section of the Mishnah of tractate Sotah:
Rabbi Phinehas ben Jair used to say: Heedfulness leads to cleanliness; cleanliness leads to purity; purity leads to abstinence; abstinence leads to holiness; holiness leads to humility; humility leads to fear of sin; fear of sin leads to saintliness; saintliness leads to (the possession) of Divine Inspiration; Divine Inspiration leads to the Resurrection of the Dead; and the Resurrection of the Dead comes through Elijah of blessed memory, amen.
Rabbi Eliezer Posner