In Method 2, there are likely chances that the grid need not be solved completely. Suppose in row 3, you know there is 1 mine, but you dont know which one, either R3C5 or R3C6, you need not find the mine to enter the answer key. This is just an example. The actual puzzle may not have it like this I'm sure, but one needs to be really careful in choosing the row/column.

I would go for Method 3.

I like Method2 because it is less typing. Obviously, depends upon specific puzzle.
Method3 is also okay.

Method1 is definitely discouraged.