...just because I prefer bestowing formal names, just in case the child decides to be addressed by his formal name, for whatever reason.
On a personal note, I love the name
John. Despite being ultra-common in my area, it reminds me of my favorite musician,
John Rzeznik.
Jack is nice, too, but while it
CAN stand on its own, it's becoming quite trendy. So, my vote goes to
John, with possible nn of
Jack.
As for the styles going together: I think
Henry and John/Jack go very well, and Finnegan/Finn and
Kiefer also work, but all the names together are a touch different (though
Finnegan, with the nn of
Finn, could also go well with
Henry and
John). However, it's not horrible clashing at all, so I wouldn't not use them.