What is the best way of adding a greater than 0 validator on the client-side using MVC and data annotation?

You can't store a number bigger than what your underlying data type could hold so that fact that the Range attribute requires a max value is a very good thing. Remember that ∞ doesn't exist in the real world, so the following should work:

[Range(1, int.MaxValue, ErrorMessage = "Please enter a value bigger than {1}")]
public int Value { get; set; }

I found this answer looking to validate any positive value for a float/double. It turns out these types have a useful constant for 'Epsilon'

Represents the smallest positive System.Double value that is greater than zero.

    [Required]
    [Range(double.Epsilon, double.MaxValue)]
    public double Length { get; set; }

You can create your own validator like this:

    public class RequiredGreaterThanZero : ValidationAttribute
{
    /// <summary>
    /// Designed for dropdowns to ensure that a selection is valid and not the dummy "SELECT" entry
    /// </summary>
    /// <param name="value">The integer value of the selection</param>
    /// <returns>True if value is greater than zero</returns>
    public override bool IsValid(object value)
    {
        // return true if value is a non-null number > 0, otherwise return false
        int i;
        return value != null && int.TryParse(value.ToString(), out i) && i > 0;
    }
}

Then include that file in your model and use it as an attribute like this:

    [RequiredGreaterThanZero]
    [DisplayName("Driver")]
    public int DriverID { get; set; }

I commonly use this on dropdown validation. Note that because it's extending validationattribute you can customize the error message with a parameter.