ProdigalSon, I don't envy your situation. And as an Orthodox who married a woman who at the time was Roman Catholic, I am very familiar with the dilemma. Thus I have some opinions on what you & others have stated.
First off, the Catholic church recognizes all sacraments performed in an Orthodox church as valid. Thus your wife could get married in an Orthodox church without any sacramental penalty. But you, as an Orthodox Christian, are not in the same situation. Should you get married outside of an Orthodox church, you are thus facing excommunication for not having your marriage recognized in the Orthodox church. This wouldn't be a problem if the Orthodox churches recognized Catholic sacraments as valid. But there is no agreement among Orthodox churches as to whether Catholic sacraments are valid. (Trust me, I've been doing research on this for years - this is actually one issue that divides Orthodox churches).
So my recommendation is to get married in an Orthodox church. Or you could have two marriage ceremonies, which is what my wife & I did at that time.
First, your questions:
"1. What Orthodox church?"
It shouldn't really matter. If you are married in an SCOBA-affiliated Orthodox Church, (Greek, OCA, Antiochian, Serbian and now ROCOR) that marriage will be recognized by all other Orthodox churches.
As for your locale, I'm sure there are plenty of Orthodox churches in and around Pittsburgh? As I understand, Pennsylvania is a state where Orthodox churches abound. Where I live, in the Great Plains (central Midwest) Orthodox churches are much harder to come by. Go to the websites of the Greek Orthodox Church, Antiochian Orthodox Church, and OCA and look under Pennsylvania. I'll bet that you can find an Orthodox church somewhere near where you're at in Pittsburgh.
"2. How about Greek Catholic/Byzantine Rite churches?"
As stated by others, to an Orthodox point of view, those are no different than other Catholic churches.
"3. How amenable are Orthodox parishes to allowing physical decorations (flowers, etc) to the inside of the church?"
Depends on the priest.
"4. How amenable are Orthodox parishes to any potential requests regarding the service or things related to the traditional American wedding? (like flower girls, the father walking the bride down the aisle, etc)"
I wouldn't count on it. An Orthodox marriage ceremony is different than a western wedding ceremony. Best to think of the two as different events. For instance, in an Orthodox wedding, there are no vows.
One thing that my wife and I really liked about the Orthodox wedding ceremony was the fact that the father does not "give the bride away" during the ceremony. Instead, the couple walk down the aisle up to the dais, arm-in-arm. Also, an Orthodox wedding has a "koumbaro" or sponsor, which doesn't really have an equivalent in a western wedding.
Second, I'd like to respond to something Serge wrote:
"Each church requires them to be raised in it because each claims it's the one true church."
When my wife & I received counseling in both the Catholic and Orthodox churches, neither priest required us to promise to raise our children in that particular church. If they had done so, that would have caused us both serious problems.
At the time that my wife was married, we had not decided upon which church to raise our children in. I was amenable to the idea that the children experience both churches, and for them to choose themselves.
But my wife, in her wisdom, decided this could send a confusing message to the children. She took a look at the Orthodox church, liked what she saw, and converted (I put no pressure upon her to do this). In retrospect, this was a good idea. As Serge said, since both churches consider itself to be Christ's one true church, both claims thus exclude the other.
Having said that, I'm going to give you different advice than what others here have written: If you're as of yet undecided as to which church to raise your children in, don't force the issue. These things have a way of working themselves out, if you give it time and listen to what Christ is calling you to do. Don't make any demands or issue any ultimatums. If you feel that God is calling you to get married soon, do so and God willing, eventually you both will decide where to make your church home (just as you will eventually know where to buy a physical home). Just make sure that any conversations you have about this are conducted in an atmosphere of mutual respect and love. I did that approach and it worked for us, and I'd recommend that approach to any others.