When I started, the instructor recommended using Dual Duty all-purpose thread by Coats & Clark.
I still use it.
My daughter had a quilt on her bed for 10 years - she also had big dogs - areas of the fabric have worn away, but I did not notice any damage along the seam lines. The Kona cotton fabric also survived well. What wore out was a tiger print on a fine feeling cotton.
Try sewing a couple of practice seams with various fabrics and various colors of thread. . I think I would match the thread to the background because it looks like there is a lot of it.
I don't much like to change threads or wind bobbins. Takes only seconds to do either one, but I still don't like ot.
For multi-color stuff, I use a color called "smoke" - or a light olivy greed.
The smoke looks like the color of the easter-egg-dye after it's gotten all muddied up.