Flowers that suit a new start
A peony is the celebratory default — full, warm, and it does not look like an apology. Add a carnation if you want it to read as steady support rather than pure celebration.
For a promotion inside the same team, keep it smaller. A single tulip with a short note is less politically awkward than a large arrangement that their colleagues will hear about.
What to write
The job is the news; the grind is the story. “Six months of applications and one very bad Thursday” says more than any congratulations line, because it proves you were watching before it worked out.
If they were treated badly at the old place, do not relitigate it in the note. The point of the message is the door they are walking through, not the one that closed.
The night before matters
Send it the evening before the first day. That is when the nerves are real and a message that is not about logistics actually helps.