If I'm making a large, fully open rose with wired petals, what gauge wire do I need for a) the petals and b) for the bud to be mounted on?

For a large rose (more than 3 inches in diameter) I use a 18 gauge. The end result will be heavy.

I only wire the last (or two) rows when I do an open rose. For these I would use a 28 or 26 gauge.