C# – the best data type to use for money in C#

string is an alias in C# for System.String.
So technically, there is no difference. It's like int vs. System.Int32.

As far as guidelines, it's generally recommended to use string any time you're referring to an object.

e.g.

string place = "world";

Likewise, I think it's generally recommended to use String if you need to refer specifically to the class.

e.g.

string greet = String.Format("Hello {0}!", place);

This is the style that Microsoft tends to use in their examples.

It appears that the guidance in this area may have changed, as StyleCop now enforces the use of the C# specific aliases.

In C# 5 and earlier, to give auto implemented properties an initial value, you have to do it in a constructor.

Since C# 6.0, you can specify initial value in-line. The syntax is:

public int X { get; set; } = x; // C# 6 or higher

DefaultValueAttribute is intended to be used by the VS designer (or any other consumer) to specify a default value, not an initial value. (Even if in designed object, initial value is the default value).

At compile time DefaultValueAttribute will not impact the generated IL and it will not be read to initialize the property to that value (see DefaultValue attribute is not working with my Auto Property).

Example of attributes that impact the IL are ThreadStaticAttribute, CallerMemberNameAttribute, ...