What should I chant when offering obeisances to home Deities and temple Deities?
Generally, when paying obeisances to the Deities anywhere we offer obeisances to the Guru because by guru's grace we have some association with the Deity, then you can offer whatever prayers to the Lord you prefer from the Srimad-Bhagavatam, Brahma Samhita etc.
If you are not initiated then offer pranams to Srila Prabhupada:
namah om vishnu padaya krishna presthaya bhu-tale
shrimate bhaktivedanta swamin iti namine
namaste sarasvate deve gaura vani pracharine
nirveshesha shunyavadi paschatya desha tarine
Hope this is helpful