Your dogwood tree would certainly benefit from some pruning, rather not leaving it to nature, a few pruning cuts will benefit its structure in the long run. 

You do have the right idea regarding this split going up the stem. You do want to choose a central leader to lead growth, and subordinate (suppress) any competing growth. I however would not choose the little guy despite being in the center, but rather the strongest, fullest, most dominant shoot. I feel I would choose the front one on the right, and reduce the other 3 by about half. I would also absolutely subordinate this elongated growth coming from either side of the tree, this growth is excessive and should be cut back. The growth growing up from the lateral branches I'd cut back to about where the 4 split begins, if that makes sense, always cutting back to a healthy bud. I believe this would greatly improve the structure of the tree going forward! 

Furthermore, if you were to top the four leaders with the intention of the little one in the center taking over, I believe you would be dealing with a lot of water sprouts, for quite some time, with the tree looking structurally awkward in the process, though it may work out in the end. 

Best of luck!

Now is a fine time to prune, no need to wait unless it's for a warmer day to do it! 

It looks like leaf scorch. I can tell because it's generally the ends, and outsides of the leaves that've been effected. Dogwoods are in nature understory trees, and can suffer during periods of prolonged sunshine and heat. During these periods providing additional water and or shade if possible during afternooon hours can help alleviate these symptoms.

https://mortonarb.org/plant-and-protect/tree-plant-care/plant-care-resources/leaf-scorch/