In Star Trek - The Motion Picture the V'Ger entity takes Ilia to use as a template with which to make its probe for interface with the crew of the Enterprise. Is there an in universe reason as to why Ilia was chosen over any other member of the crew? Did her being a Deltan contribute to V'Ger's choice somehow? Or was it simply a random decision?
Long answer, but for those unfamiliar with Star Trek: Phase II, I think you'll find some details interesting. (Plus I recommend a really cool book you can get on Amazon that even contains a rough draft from the 1970s for what became a ST:TNG episode!)
It was random, like the 1,000th person over a bridge or because she was there.
There's also a behind the scenes answer to that. While I prefer to keep answers in-universe, this will help in understanding what happened.
The original plan was to make a new series, Star Trek: Phase II, about a new five year mission. Nimoy wasn't going to sign on and a new Vulcan named Xon would replace him. Also, there was going to be an Executive Officer, Will Decker, and a ship's counselor, Ilia. (Yes, this was in the 1970s and some of the ideas for Star Trek: The Next Generation were already taking form.)
I can't remember if it was a deleted scene or just in the book, but there was a scene with Kirk meeting Xon and telling him to prepare to beam over to the Enterprise. He's one of the two crewmembers involved in the transporter accident where we hear, "What came back didn't live long." And, of course, we do see the characters of Will Decker and Ilia. (Hmmmm... a dashing young man as a First Officer with a past relationship with an alien with some advanced mental abilities who is now the ship's counselor -- sound familiar?)
These three characters were new to the series for Star Trek: Phase II. (You can read a lot about that series, including some scripts and story outlines in Star Trek: Phase II : The Making of the Lost Series)
But things changed and, after another TV show from the 1960s was remade into a movie, Paramount decided they wanted to do the same with Star Trek, so they decided that instead of a second series, they wanted to do a movie. (And if the movie worked, they could do sequels or use it to start a new series.) They took a two hour script that was supposed to be the pilot for Phase II, titled In Thy Image (by Alan Dean Foster) and re-wrote it for the big screen.
(This rewrite of a 2 hour TV teleplay for a big screen movie explains a lot of the weaknesses of Star Trek: The Motion Picture and why, sometimes, to add FX, they just ran some scenes WAY too long. They already had a script and story and it was easier to just add FX scenes than alter the story any more than they had to.)
So they were shooting a movie with a script that was based on a pilot for a TV show. They killed off Xon, so Spock not only got his lines, but the extra bit about going into V'ger, they added the conflict between Decker and Kirk, and changed Ilia to a navigator, since it would be too hard to explain the position of a Ship's Counselor in a one-shot movie.
The movie was now a set-up for a Trek universe that was as close as possible to the original series. There was no reason to keep Ilia on the crew, so it was easier to use this new character as the "guinea pig" for V'ger and also set up an ending that made it easy to remove both new characters and leave the Enterprise crew as it was in the series.
At this point there was no need to give a reason for V'ger's choice of Ilia over any other. She was, essentially, a red shirt and so was Decker.
So the in-universe reason was random choice. The behind the scenes reasoning was a little more in depth.
Oh, just as a bit of trivia, yes, the intent was that Will Decker was the son of Matt Decker, who sacrificed himself to try to kill the planet killer in The Doomsday Machine.