As to ME and I, for proper usage separate them.
Randy and me are going to the movies for example. Separate them to:
"Randy is (singular for are) going to the movies" is good but "me is going to the movies" is bad.
John is going to the movies with Randy and me:
"John is going to the movies with Randy" is good and "John is going to the movies with me" is good also.
Randy and me are going to the movies for example. Separate them to:
"Randy is (singular for are) going to the movies" is good but "me is going to the movies" is bad.
John is going to the movies with Randy and me:
"John is going to the movies with Randy" is good and "John is going to the movies with me" is good also.