I think wrist movement will change depending on a lick or exercise. This also depends on you as an individual, cause I believe the way we hold a pick can be quite unique. What works for you wont necessarily work for others.
Generally, if this is about alternate picking (Hard to tell what genre from the title), then the less movement the better. This can be achieved just by going a little slower, so you can really build that muscle memory you have. For the purpose of any alternate picking exercise, attempt any exercise really slowly, with least movement possible – you will realise just how much movement is required in order to get a noise from a picked string.
I’m a huge fan of rammstein, and find that they use alot of down motion picking to get that rammstein sound. You will find with Rammstein that they will have big movement in order to achieve a real punchy, aggressive riff – and this sounds great! Listen and learn the repetitive riff from Rammsteins song ‘Asche Zu Asche’, or maybe ‘Links 2 3 4’.
Other genres such as Funk, I find I make so much movement but its required to get a rhythmic sound. I think my suggestion would be to learn a bit of Funk, maybe a bit of Hip Hop, because I think this would require a very loose wrist in order to work.
Hope this helps!