With a low budget just paint everything,i.e walls, trim and it will brighten everything up... Add a few inexpensive contemporary paintings throughout.

Keep your daughters age in mind, if she is old enough let her pick something that she likes, that is popular in relation to her age, etc and you will have a beautiful modern basement done with a reasonable budget.

Good luck

I would definitely paint the trim white and the walls light. Get a large area rug - the lighter the better and buy a felt pad to go underneath. The pad needs to be a couple inches smaller all the way around then your rug size. They are not expensive but the extra padding will help cushion any falls and make the room feel cozier. Add as much floor/wall/table lighting as possible. In basements, I always like to add some sort of faux greenery. If you can’t afford to repaint the walls, add large white background canvas art. Wayfair is my go to as their art typically comes in different sizes for the same piece.