Good grief! Please don't "just guess" and then post. A 500 lb., 15 hand horse would be about dead. Besides, we can't offer helpful advice if we don't have a somewhat clear picture of the situation. Okay, I'm done barking at you.
She's on the light side but not a bone rack. How you feed depends on what her activity level is. Does she mostly hang out in the pasture or do you ride and exercise her? Some horses are easy keepers and others take a feed store to keep them up. There are many factors to consider. And you are going to get many different opinions here. Personally, I prefer a good grass hay but many people feed alfalfa. And do be careful about supplements. It's easy to by stuff because it sounds so good for them but may not be needed and over-supplementing can be harmful.
I prefer to get the opinion of a vet with a new horse. A checkup is a good way to start. Get a weight tape. They are not exact but it will help you track weight gain and loss.
Good luck to you. I hope you and your horse have many good years together!
And welcome to the board. : )
If you ever find yourself in a fair fight, it's because your tactics suck. ~ Marine 1SGT J. Reifinger