Should I pray the 'Ishā prayer with those who are late, or should I wait for the Imam to pray it with him with the intention of the 'Ishā prayer when he begins the Tarāwīh prayer?

If you find a congregation that has missed the 'Isha prayer and the Imam has not yet begun the Tarawih prayer, it is best for you to pray the 'Isha prayer in congregation first, and then join the Imam for Tarawih. This is to attain the virtue of congregational prayer and to avoid the differing opinion of those who do not permit a person performing a fard (obligatory) prayer to follow someone performing a nafl (supererogatory) prayer. However, if you find the Imam has already begun the Tarawih prayer, it is permissible to pray behind him with the intention of performing 'Isha, and you should complete your prayer after the Imam has concluded the first two rak'ahs.