Champion Jogbra continues to be the most often-mentioned sports bra by my readers. Their MCR Fit Center guides you to the best bra for your activity. They give special attention to classic compression, natural shaping, strap comfort, underwire support and moisture control. Straps that don't stay on the shoulders when you are in motion. Straps that don't work well with your backpack, resulting in double-rubbing.
Wider straps can help distribute the weight, resulting in less digging-in.
One solution commonly seen are racer-back bras without hooks, they just slip on over the head. The problem then becomes how to get the wet, sweat-soaked bra off after a good walk. If you are prone to sweating while walking, look for a wicking fabric such as CoolMax or polypropylene in a sports bra. This gives you the versatility to take your shirt off if you overheat. Most sports bras come in a variety of colors and patterns.