Is it ever proper to use myself and when starting a sentence? Here is an example of what I mean:
Myself and some very successful people are building a team across the Globe!
or Myself and (Name) are going to be on the call tonight.
You're use of the word myself is incorrect. Myself is a reflexive pronoun, that is referring back to something, most often the word I.
In the example you gave, the proper use would be,
Some very successful people and I are building a team across the Globe!
OR
(Name) and I are going to be on the call tonight.
Usually, the first person pronoun is used after the others, even though it is grammatically correct to use it the other way. Never do so, though.
Myself can, in some instances be used at the beginning of a sentence, even though not in the sense you said.
This is used to emphasis your own role when giving your opinion.
Myself, I can't stand cheese.
However, this is only accepted in informal speech, and its use in formal language should be avoided.