Welcome to the forum.
I am a godmother four times!
Congratulations on the new grandson! What a blessing!
When my godsons were baptized they wore a new white gown. I say "gown" versus "suit". Keep in the mind the baby will get anointed several times, on his head, chest, hands, feet, etc... therefore, the gown makes for ease of access to the baby's body. The suit will get in the way.
Plus, the baby might get "dunked" in water, if the church has a baptismal font. Again, the gown would be easier to take off.
As far as I know...the gown should be white - pure and innocent. A blanket to wrap him in would also come in handy - again white.
A blessed cross (baptismal cross) should be presented to the child by his godfather. This cross will be with him his whole life.
The baby will also have a snippet of his hair cut and burnt on a candle as his first "offering" to God.
The priest will also take the baby, as he is a boy, into the altar at the very end.
You can offer the "monetary gift" to the priest discreetly. He may or may not take it, but, you should offer it (after all, he too has bills to pay).
Let me share one really special moment....I always got goosebumps and started crying as the priest led us, holding the baby, around the tetrapod three times. These are the baby's first steps as a baptized member of the True Church, supported by his godparents, led by his shepherd and pastor. They say that at that moment all the Heavens rejoice and the angels sing with joy. The thought of all the angels singing, was always so humbling to me, that I never made it to the end without tearing up and shaking.
Here's a good article on what to expect:http://www.ehow.com/how_2325487_be-baptized-greek-orthodox-church.html