Enum vs string const class

I have a string property, which will accept some kind of enum
Is it better to have a proper

Enum

Enum

and call

ToString()

ToString()

when setting the property (

public enum StatusEnum

public enum StatusEnum

and set it

p1 = StatusEnum.Status1.ToString()

p1 = StatusEnum.Status1.ToString()

), or should I have a static class which will have constants, something like this

public static class StatusEnum
{
    public const string Status1 = "1";

public static class StatusEnum
{
    public const string Status1 = "1";