Question: I have seen many (GENERAL, BEGINNER TYPE) definitions, however, the actual meaning of a sentence I have yet to find, that is non-specific to a particular domain. This would be useful since a statement is defined in terms of a sentence and is one of the first concepts I am introduced to.

Answer: 
I would say most texts don't make a difference between the two. In fact: statement, sentence, claim, and proposition are typically all seen as the same thing: something that has a truth-value.

If a text does make a distinction, I suspect it might be between the syntactical expression that we use in order to express a claim, and the claim itself as more of an abstract idea, in much the same ads a number can be expressed in different ways: a numeral is what represent a number. Likewise, one could see a sentence as representing a statement or claim.
In some treatments of mathematical logic where quantified variables appear in the formulas of a language, *statement* may refer to any formula while *sentence* refers specifically to a formula without free variables (i.e. variables not bound by a quantifier). So a statement may say something *about particular objects* under an interpretation of the free variables, while a sentence makes a "general" statement independent of the interpretation of free variables (though it may still say something about particular objects which are *definable* in the language without parameters). However, this is just one convention for the use of the words "statement" and "sentence" and other treatments may use the words differently.