In today's time most of the worship/rituals that are done are done based on the injunctions of the Tantras. Sometimes the Puranic methods are also followed ( for e.g. Durga Puja in Bengal). Sometimes a mixture of methods.
And, in this style of worship, Lord Ganesha usually is invoked/appeased first. That is why he is called "Prathama Pujya".
But in a Vedic fire ritual, is there a deity which is to be invoked/appeased first? Of course Agni is to invoked first otherwise the ritual will not even start.
But apart from him, is there a rule that a particular deity must receive the first Havi (oblation)? Like say Brahmanaspati, Varuna or any other?