Wrys and Lissa actually have the strongest healing staff, Rehabilitate. Wrys in particular also has a Special Skill that heals your other two allies for 10 HP when you heal someone else, so in terms of pure healing he is the strongest.
For utility, Elise reigns supreme. Recover's 15 HP is stable and reliable, and strong enough to be game-changing. She also has the Attack boosting Balm, and is mounted for more Mov. Her Gravity staff is very useful on maps with obstacles, such as the lava map and the water map. Clarine is also usable, but requires her to take damage first to be truly effective.
If you want a staff unit who focuses more on support instead of full healing, Sakura or Maria are good picks. I personally prefer Sakura, but people rate Maria higher because of her survivability.