In general, best to ask your priest for detailed instructions, because every Church has different facilities/fonts/layouts, and that could present unique situations. Also depends somewhat on your parish's liturgical tradition (Byzantine or Slavic).
In fact, you really need to go over the game plan beforehand with the priest and your son's sponsor(s), because during the anointing with the Oil of Gladness and the Baptism itself, you'll have an oil-coated, wet baby, and y'all will need to know who is supposed to hold him at what time and how best to hand him off and how best to use his sheet to keep the oil off yourself. It's not hard, but it requires a bit of planning.
Does he wear a baptismal gown?
Many parents (and grandparents!) like to get a nice baptismal gown. Makes for nice pictures. If that sounds like you, feel free to get one.
If you go that route, do one of two things: (1) Just don't put it on your son until after the Baptism is complete; or (2) Check with the priest to see if the church has an acceptable place for you to take the fancy gown off of your son after the initial part of the ceremony. There's no reason why your son can't be all decked out for the part that takes place in the Narthex, but pretty soon after you enter the nave and approach the Baptismal Font, your son needs to be completely undressed and wrapped in a sheet/cloth.
Are there special items to give to him as gifts?
He gets a cross to wear around his neck from his sponsors. It's also typical nowadays to get him an Icon of his patron saint. Here is an excellent article on the all the various aspects of the Christening: http://www.saintbarbara.org/faith/sacraments/baptism/baptism.cfm
As you can see, they'll be a LOT more than just a Baptism. It's really a full entry into the Church -- Baptism, Chrismation, Communion, plus some more.
The priest will also take the baby, as he is a boy, into the altar at the very end.
This is not done in the Byzantine tradition, or in any of the Slavic churches I have attended. Is this a normal Ukrainian thing, or are you thinking of the Churching?