"I will make me a ..." or "I will make myself a ..."

I will make myself... is correct.

I can't think of any sentence at all where I will make me would be grammatically correct.

Here's why: "Myself" is the reflexive form of "me", for use when you've already used the pronoun (in this case, "I") in the sentence and are referring back to it. For example, I'd say "you can make a sandwich for yourself", rather than "you can make a sandwich for you", since I already referred to you (by using the word "you") in the sentence.

I will make me, means I will make something for me.. A sandwich, a cake ect.

I will make myself, means I will put myself in a position to be.. available, ready, ect.

The second form is valid. Also valid is:

"I will make a sandwich for myself"

"I will make me a sandwich" sounds at best unnatural to my ear -- at worst ungrammatical -- as long as you make a sandwich for someone, but definitely make a sandwich for yourself.

And so:

Can you make me a sandwich?

Can you make a sandwich for me?

But, use a reflexive pronoun if and when you want to emphasize that the subject does the action.

I'll make myself a sandwich.

I'll make a sandwich for myself.