Is there any reason Jane chose a feminine persona for herself? Did she choose at all?
Jane answered that when conversing with Milo in "Children of the Mind":
“I’m not as set on using Val’s body as you were to have me do it,” said Jane. “Peter’s will do as well. Even Ender’s, as long as he’s not using it. I’m not actually female. That was merely my choice of identity to get close to Ender. He had problems bonding readily with men. The dilemma I have is that even if Ender would let go of one of these bodies for me to use it, I don’t know how to get there. I don’t know where my aiua is any more than you do. Can you put your aiua where you want it? Where is it now?”
I don't think she chose. In Xenocide,
it's revealed she was created by the Hive Queens connecting to the Fantasy Game at Battle School. So I expect she was born that way. It's possible that when the Hive Queens pulled her aiua in to the universe from Outside, they pulled a lady-aiua, as that's what all the Hive Queens are.
Her sex was actually established by Ender in First Meetings, when she offered him the choice of either male or female avatars. As a computer/god, she has no inherent sex. Aiuas also have no inherent sex, just a desire to hold the pattern.