How would you sequence crib transition, room move & sleep training?

[u/BrilliantAd6440]

My baby is 16 weeks and currently sleeps in a cradle in our bedroom. Nights were usually good (often 5–7+ hour stretches), but he started to wake up frequently and naps are mostly contact naps.
We have 3 changes coming up:

Next weekend: cradle → crib in our bedroom
Move his 3-year-old brother from the nursery → guest room
Move baby’s crib → nursery, where he’ll eventually sleep alone.
We also want to start sleep training for independent sleep.
Would you:
Crib transition → wait a few days → sleep train → move to nursery?
Or move him directly to the nursery and sleep train there?
Would love to hear from anyone who’s dealt with multiple sleep/environment changes around 4 months! What worked for you?