Does Column Order Really Matter?

Does column order really matter for Query Optimizer to pick index.
Case 1:
Say my CUSTOMER table has one composite index containing FirstName and LastName. FirstName exists prior than LastName. Does the column, FirstName and LastName, order matter to have Query Optimizer to utilize the index when I write WHERE clause in a SELECT statement?
Statement 1:
SELECT * FROM CUSTOMER
WHERE FirstName = 'John' and LastName ='Smith'
Statement 2:
SELECT * FROM CUSTOMER
WHERE LastName ='Smith' and FirstName = 'John'
Will both statement 1 and 2 use the composite index or only statement 1?
Case 2:
Say my CUSTOMER has two single-column indexes. One index is on column FirstName. Another is on column LastName.For statement 1 and 2 above, which index will be picked by Query Optimizer or both? How does QO pick for index?
I read couple book and some books say column order matter but some say no. Which one should I go with?  I'm kind of confused.