If you experiment with counters, count up, not down.
If you count down, every player has to have ALL their counters, and then when they take damage, they have to physically put them somewhere else. If you have 5 people at the table, and they each have 40 hit points, you'd have 200 counters at all times.
On the other hand, if you count up, you can have a single container with 200 poker chips (or use values like white = 1 / blue = 5 red = 10) so if each player has taken 10 points of damage you only have 4-40 tokens in play. It's also easier to see that someone is getting hurt if they have a big pile of damage sitting in front of them versus having a small pile. Monkey brains are good at associating big piles with big amounts.
It's easier to track damage than health if you use a physical token.