Stethescopes don't work for everyone. Electronics are the only way to go for me.
That pictured HRM is the same one I use, works great just wet the horse. However sense you mentioned speed distance, go ahead and buy once cry once.
Get a Garmen foretrex 401, or a 310XT, these are wrist gps wich will track speed distance and also can run a HRM. They are also the only two wrist GPS that have 20 plus hours of battery life. The 310xt recharges and the 401 uses AAA's. I have the older 301 then the HRM you posted , workes well enough for me that I will wait till one or the other dies to upgrade to an all in one unit.
Buy once cry once, as you will end up spending almost the same on seperate HRM and GPS. https://www.thedistancedepot.com/Gar.../g-310xtak.htm
Another option is the etrex line of hand held GPS, way better for navigating, and then the hand held HRM you selected.