What should I say if I join the Imam after he rises from bowing?

The first thing you do is the takbīrat al-iḥrām (the opening Allahu Akbar), for the prayer is not valid without it, based on the Prophet's (peace be upon him) saying: "The key to prayer is purification (ṭahūr), its consecration (taḥrīm) is the takbīr, and its release (taḥlīl) is the taslīm." And his saying: "The prayer of anyone among the people is not complete until he performs ablution, placing the ablution in its proper places, then says 'Allahu Akbar'."

After the takbīrat al-iḥrām, if you have enough time, there is no harm in reciting the dhikr of moderation: "Our Lord, and to You be all praise." And if you add: "Much good and blessed praise," it would be even better, as it has been reported that the Prophet (peace be upon him) said concerning the one who recited it: "I saw thirty-odd angels rushing to see which of them would write it down first."