First of all-thank you for asking such an interesting question. It's a fun one to think about, and I'm almost surprised I hadn't thought of it before.
To repeat the question: "If you had to choose between purple, gray, and orange, what color would you paint your imagination?"
Off the top of my head I would say orange. Even though gray isn't a bad color, and purple seems to fit my imagination a little better, i would just say orange. It's an uplifting color that can be appealing to male and female, and I personally think it looks nice. Also, you know how when people paint something, it's not just for themselves to see, it's also for others to see? Sometimes things are painted for the sole purpose of having other people approve of it. If I painted my imagination, I would want it to be a color that shows how i want it to affect other people. For me, I want to use my imagination in a way that it can please others of either gender. Whether it be through a poem, story, joke, or even choice of quote. Orange is quite close to yellow, and yellow is often used to represent heaven. In that way, I want to point people towards God, even if it's not obvious.
So, to answer your question, I would paint my imagination orange. it's appealing, bright, and almost symbolic in a way.