In practice on typical 64-bit machines, the MINIMIZED mode is reasonably efficient, and can be generally used. It also helps to ensure compatibility with code imported from some other compiler to GNAT.
Setting all intermediate overflows checking (CHECKED mode) makes sense if you want to make sure that your code is compatible with any other possible Ada implementation. This may be useful in ensuring portability for code that is to be exported to some other compiler than GNAT.
The Ada standard allows the reassociation of expressions at the same precedence level if no parentheses are present. For example, A+B+C parses as though it were (A+B)+C, but the compiler can reintepret this as A+(B+C), possibly introducing or eliminating an overflow exception. The GNAT compiler never takes advantage of this freedom, and the expression A+B+C will be evaluated as (A+B)+C. If you need the other order, you can write the parentheses explicitly A+(B+C) and GNAT will respect this order.
The use of ELIMINATED mode will cause the compiler to automatically include an appropriate arbitrary precision integer arithmetic package. The compiler will make calls to this package, though only in cases where it cannot be sure that Long_Long_Integer is sufficient to guard against intermediate overflows. This package does not use dynamic alllocation, but it does use the secondary stack, so an appropriate secondary stack package must be present (this is always true for standard full Ada, but may require specific steps for restricted run times such as ZFP).
Although ELIMINATED mode causes expressions to use arbitrary precision arithmetic, avoiding overflow, the final result must be in an appropriate range. This is true even if the final result is of type [Long_[Long_]]Integer'Base, which still has the same bounds as its associated constrained type at run-time.
Currently, the ELIMINATED mode is only available on target platforms for which Long_Long_Integer is 64-bits (nearly all GNAT platforms).