Thanks for the advice. I haven't read over the translation and changed anything yet, because I just finished. Here's the whole thing:
Meanwhile that day Jason was seeking by means of what the messengers had said, and out of all of the many areas of Greece, they were moved either by something new or hopes of glory, and came together from all sides. Moreover having been delivered in this number was Hercules, whom many with authority have written of, Orpheus, Theseus, Castor, and many others who’s names are not well-known. Out of them Jason decided those who were the most prepared to undergo dangers, and he chose fifty of them who he joined himself to as companions. then having stayed for a few days in order to prepare the opportunity for all of the men, the ship launched, and having found that the season was suitable to about have been sailing, they set sail with much applause.
please tell me if you see anything else wrong with it.
EDIT: I've looked over the first sentance and changed it. So far I have this:
Meanwhile on the day that had been designated by the messengers...
I still cant figure out how to Iason or appetebat into it, however.