What human experience I would like Gadreel to have? Being completely appreciated and accepted for who he is, finding "a family". The happiness that comes with that feeling.
That is a big one. One I'm trying to fulfill in my fic, as well. One I know many people are trying to fulfill, actually. Haha, we're so broken.
But there are also the smaller things. Like in "I'm No Angel," though I prefer to approach the topic a little more seriously.
There are experiences that we go through every day that an angel wouldn't. Or they wouldn't think to. For instance, I have him do house chores in the shelter he's in. (Because he wants to. He wants to support himself and learn.) He vacuums, he cleans, he washes dishes. Like Castiel mentioned, there's a sort of dignity to doing these menial tasks. Because they've never had to do them before. And one such as Gadreel, who knew nothing but isolation and pain for thousands of years... Taking out the trash may very well be interesting. Because it's living.
And there was the Niel angel who said he liked The Notebook. I'm pretty sure he hadn't watched that until he got stuck on Earth and masqueraded as a person. Or Tyrus, who liked bowling.
Just these little, often trivial, things that humans do I like to imagine Gadreel experiencing. Because his angelic life kinda sucked. Maybe a human one would be better.