First off, I understand there are folk who oppose the use of singletons. I think it's an appropriate use in this case as it's constant state information, but I'm open to differing opinions / solutions. (See The singleton pattern and When should the singleton pattern not be used?)

Second, for a broader audience: C++/CLI has a similar keyword to readonly with initonly, so this isn't strictly a C# type question. (Literal field versus constant variable in C++/CLI)

Sidenote: A discussion of some of the nuances on using const or readonly.

My Question:

I have a singleton that anchors together some different data structures. Part of what I expose through that singleton are some lists and other objects, which represent the necessary keys or columns in order to connect the linked data structures. I doubt that anyone would try to change these objects through a different module, but I want to explicitly protect them from that risk. So I'm currently using a "readonly" modifier on those objects*.

I'm using readonly instead of const with the lists as I read that using const will embed those items in the referencing assemblies and will therefore trigger a rebuild of those referencing assemblies if / when the list(s) is/are modified. This seems like a tighter coupling than I would want between the modules, but I wonder if I'm obsessing over a moot point. (This is question #2 below)

The alternative I see to using "readonly" is to make the variables private and then wrap them with a public get. I'm struggling to see the advantage of this approach as it seems like wrapper code that doesn't provide much additional benefit. (This is question #1 below)

It's highly unlikely that we'll change the contents or format of the lists - they're a compilation of things to avoid using magic strings all over the place. Unfortunately, not all the code has converted over to using this singleton's presentation of those strings.

Likewise, I don't know that we'd change the containers / classes for the lists. So while I normally argue for the encapsulations advantages a get wrapper provides, I'm just not feeling it in this case.

A representative sample of my singleton

public sealed class mySingl
{
    private static volatile mySingl sngl;
    private static object lockObject = new Object();

    public readonly Dictionary<string, string> myDict = new Dictionary<string, string>()
    {
        {"I", "index"},
        {"D", "display"},
    };

    public enum parms
    {
        ABC = 10,
        DEF = 20,
        FGH = 30
    };

    public readonly List<parms> specParms = new List<parms>() 
    { 
        parms.ABC, 
        parms.FGH 
    };

    public static mySingl Instance
    {
        get
        {
            if(sngl == null)
            {
                lock(lockObject)
                {
                    if(sngl == null)
                        sngl = new mySingl();
                }
            }
            return sngl;
        }
    }

    private mySingl() 
    {
        doSomething();
    }
}

Questions:

1. Am I taking the most reasonable approach in this case?
2. Should I be worrying about const vs. readonly?
3. is there a better way of providing this information?