Congregational prayer and prayer at the beginning of its time are both considered highly recommended in Islam. In "Wasa'il al-Shi'a" has been reported from one of the A'imma, peace be upon them, that congregational prayer is not mandatory but rather a sunna, however once it has been established it is not appropriate for the believer to abandon it with no valid justification to the point that Imam said: "Who abandons the congregation of the believers with dislike without any valid reason, in fact has not prayed". Another narration from the same source on the authority of Imam al-Sadiq, peace be upon him, says: "For each salat, there are two times and its first time is the best one. No one should delay it until its last time unless he has a valid justification". Regarding more specifically your question, considering that praying 10-20 minutes later may still be considered as "its first time" according to the 'urf, by waiting for your family you would get the blessing of both congregational prayer and prayer at the beginning of its time.  You may also use those 10-20 minutes for preparing a suitable environment for the Jama'ah and recite some adhkar.

With prayers for your success.