Me, Myself, and I

When I was a little girl, my mother used to sing a song about someone, so conceited that her only playmates were me, myself and I. I don't remember the tune or the words but the concept of one's favorite companions being only themselves stuck with me all these years.
In proper grammar circles, me, myself, and I are sentence objects and subjects that can be quite confusing when constructing a sentence.
"Me, myself, I hate goat cheese."
The previous example uses all three subjects and objects in a sentence. as you can imagine though, it isn't correct.
I, being the subject of the sentence is used correctly. Even the use of myself in this scenario, is appropriate because it emphasizes the subject of the sentence...'I'.
Beginning a sentence with me, the object of a verb, before there is a verb, is incorrect.
Let's look at some examples-
I, myself, don't like ham and cheese.-correct
I, don't like ham and cheese, myself.-correct
'myself' in these situations emphasizes the subject.
The ham and cheese were disliked by my brother and I.-incorrect
Ham and cheese isn't the thing to serve my brother and I.-incorrect
The subject is 'the ham and cheese'. alone in the sentence the object of the verb dislike or serve is me, not I.
If you begin a sentence with a combination like...my brother and me it is the same whether or not me, or brother come first.
i.e. 'I and my brother don't like ham and cheese.-correct
"My brother and I don't like Ham and Cheese.-correct.
Me and my brother don't like Ham and cheese.-incorrect
My brother and me don't like ham and cheese.-incorrect
The arrangement of the subjects doesn't change the grammatic correctness.
It sounds awkward to say 'I and my brother' and therefore wouldn't naturally appear in most people's vocabulary. The truth is though, it is correct.
Often basic grammar mistakes are made because they sound backward or awkward. Using 'me' because it sounds better than I, or visa versa, is a social adjustment speakers make to smooth out their speech.
'The suitcase arrived beside my wife and I.' incorrect
'The suitcase arrived beside my wife and me.' correct
You wouldn't say 'the suitcase arrived beside I.' and therefore you wouldn't use I as the object in the sentence in combination with 'my wife'.
If there are questions about this, remove the first subject and leave me or I and the correctness of the sentence becomes obvious.
I was taught that myself was reflexive, meaning it should be used to emphasize the original subject. 'Myself' is a little harder to grasp.  If you'd like further references look up grammargirl.com or grammerly.com and keep writing!