What's the best part of your hand to hit the handball with

Right in the lower middle of your palm. It get is a flat shot when the ball hits the wall.

l would think the hand.

If u use clenched fist, it is on the back of the middle phalange of ur 'middle' fingers - meaning, the 2nd last phalange of the closed 'fist'. This is used when creating power.
When using the palm side of the hand [as in open handed play], one usually gains better control re spin, touch & deceptive shaping of the hand when the ball is contacted in the mid-pads or end pads of the fingers.
Also, with a lot of controlled shots with good follow-through, if u really had a finely-tuned camera & film, u would see that the ball actually initially contacts the base of the palm of the hand & rolls all the way along the insides of the fingers towards the tips, finally leaving the hand completely from the finger tips.
The ball does not just hit a hard surface at one point & then deflect from the surface.
These factors apply for any ball game where a ball is contacted by the human hand, & then delivered from it.

sumwhere around your palm