In general, the rule of thumb is that prefix and postfix operators don't mix well in a single expression - order of operations is confusing, and reading the code requires going back and forth to follow it.
In the ideal world, we wouldn't have unary prefix operators at all, but unfortunately unary +, -, and NOT are prefix mostly because they were that in math notation and got grandfathered in (bonus points to Smalltalk here for going with consistency here - "not" and "negated" are regular nullary methods there so it's postfix throughout!). However, these are rarely themselves an operand of another unary operator, so you can mostly deal with this by giving postfix higher precedence than prefix in all cases, so at least it's a simple rule. But then for pointer dereference, it is in fact common to have the result of a dereference itself be an operand in the middle of another expression.
So now you have some choices to make. If you make the pointer dereference prefix, then you don't need extra parentheses when applying other prefix operators to it, e.g. -*p or !*p. If you make it postfix, then you don't need extra parentheses when applying other postfix operators to it, e.g. (using Pascal-style ^ for dereferencing) p^[0] or p^.x. Alternatively, you could add special postfix operators that desugar into the combination but avoid those extra parens, which is what C did with -> for field access.
(Technically, you could also make everything prefix instead, e.g. field access ALGOL 68 style: `month OF birthDate OF person`. But this is very counter-intuitive with indexing, and also makes code completion unusable, so it's not a serious option.)
In the ideal world, we wouldn't have unary prefix operators at all, but unfortunately unary +, -, and NOT are prefix mostly because they were that in math notation and got grandfathered in (bonus points to Smalltalk here for going with consistency here - "not" and "negated" are regular nullary methods there so it's postfix throughout!). However, these are rarely themselves an operand of another unary operator, so you can mostly deal with this by giving postfix higher precedence than prefix in all cases, so at least it's a simple rule. But then for pointer dereference, it is in fact common to have the result of a dereference itself be an operand in the middle of another expression.
So now you have some choices to make. If you make the pointer dereference prefix, then you don't need extra parentheses when applying other prefix operators to it, e.g. -*p or !*p. If you make it postfix, then you don't need extra parentheses when applying other postfix operators to it, e.g. (using Pascal-style ^ for dereferencing) p^[0] or p^.x. Alternatively, you could add special postfix operators that desugar into the combination but avoid those extra parens, which is what C did with -> for field access.
(Technically, you could also make everything prefix instead, e.g. field access ALGOL 68 style: `month OF birthDate OF person`. But this is very counter-intuitive with indexing, and also makes code completion unusable, so it's not a serious option.)