Set-once-properties violate the principle of least surprise - a caller expects that when a property can be set once, it can be set again. (barring range and compatibility checks, of course - but they are bound to specific values or value combinations).
Initialize them in the constructor.
Alternatively, if they are to many / to complex to write all constructors, use a factory/builder class:
ThingieBuilder tb = new ThingieBuilder();
tb.FooThingy = 17.23; // r/w properties
tb.BarThingy = 42;
tb.UseExtendedThingamagicAdapter = true;
Thingie t = tb.Create();
if (t.Bar==42) // r/o property
...
Or, separate the settings in a configuration object, that can be replaced or passed during construction.
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