Basically, in addition to "no stamina cost when sprinting or jumping" and "sprinting and jumping consumes stamina", I'd like to suggest a third option: Stamina can be consumed for an enhanced sprint.

Under this setting, sprinting while you have stamina would consume stamina, and you'd get additional speed out of it as long as you have stamina to consume. Running out of stamina would drop you back to a normal sprint. Jumping would also be enhanced--maybe you'd get an extra half a block of air with a stamina-enhanced jump.

(This idea came to me when I was building a modpack around a zombie apocalypse theme, with a mod that lets zombies 'sprint' by giving them intermittent Speed II. Limiting your sprint would make it impossible to get away from zombies under these conditions, but if you had an enhanced sprint for a short burst that would play really interestingly.)