The semi-reflexive object is grammatically extraneous, but it can add a spectrum of stylistic color. It can sound "hillbilly" or ethnic. It can also mark determination when used with future or past tenses. I guess that could reflect a sense of pride in accomplishment.
While I use it for effect on rare occasions, strictly speaking I would not include it in standard English.
I agree with Glenn that its use is extraneous. Here's another way to look at it.
I've gotta' get my wife one of those things. Â No problem here.
I've gotta' get one of those things. Â Also no problem since the "me" (or properly "myself") is implied.
However, the insertion of "me" is very common in informal speech. I'm reminded of the scene in Independence Day, when Will Smith's character, used to flying "mere" F-14s, pilots the alien saucer into space and is amazed at it's acceleration and maneuverability. He exclaims "I gotta get me one of these!" In the heat of the moment, the informal structure works well to emphasize his personal desire to own a vehicle like that. One of my favorite scenes in that movie. I soloed in a measly Cessna, never flew again, and always dreamed of what a military jet must feel like.
I think the verb get might be considered among a few special cases. It is ditransitive (valency of 3) and can take two objects without prepositions. The indirect object always comes first, followed by the direct object.
I'm giving my wife a bracelet.
I bought my son a baseball.
I will bring my colleague a coffee.
I'm getting my daughter a car.
I took them a bottle of wine.
Back to the original topic, you can easily use a reflexive with these ditransitive verbs, but for standard English, it should be a standard reflexive pronoun.
I'm giving myself a gift.
I bought myself a new pair of shoes.
She got herself a circular saw.
In the stylistic use, the indirect object position is filled with a nonreflexive pronoun. This is seen most clearly in the first person, but also applies to second and third, a bit ambiguous in third person.
I gave me a good bump on the head. (Standard: I gave myself a good bump on the head.)
He got him a good wife. (Standard: He got himself a good wife.)
You bought you a world of hurt. (Standard: You bought yourself a world of hurt.)
In this stylistic construction, verbs that are not typically ditransitive are also treated as such, but only in reflexive use. The verbs eat, hear, and see, for example, are not typically ditransitive, but are used as such in this colorful construction. In these cases, there is no standard version, since the use of the reflexive pronoun is also stylistic.
He's eating him a filet mignon. / He's eating himself a filet mignon.
She's seeing her a movie. / She's seeing herself a movie.
They're hearing them some guitar music. / They're hearing themselves some guitar music.
I learnt me new words from context ( without checking a dictionary): valency, reflexive pronoun, reflexive use, ditransitive, stylistic use, colorful construction. How neat!