A female's monogram is traditionally done in FIRST/LAST/MIDDLE (or MAIDEN) order with the center initial larger than those on the sideS.

Sarah Claire Doe = s D c

Monograms for a gentlemen are traditionally in FIRST/MIDDLE/LAST order with the letters the same size.

Michael Thomas Jones = MTJ 

 A more modern approach to a gentleman's monogram is to stack the  FIRST and MIDDLE initial with the LAST NAME initial larger and to the right

 A gentleman may prefer the

FIRST/LAST/MIDDLE order

(as shown for female), but this is usually  reserved for male babies and children.

Michael Thomas Jones = m J t 

When Sarah and Michael get married, their couple's monogram is done with her initial first, their surname initial larger and centered, with his first initial on the right.

Sarah Claire Doe marries Michael Thomas Jones = s J m Sarah + Michael Jones

In certain instances, couples prefer to have the gentleman's initial first with hers on the right. That is perfectly fine depending on preferences and should the letters look better with that arrangement.

For babies, traditional rules apply, but many times, the first name only is used for personalization.  The first letter of the name may or may not be capitalized according to preference.