Need to change phone number

[apl3]

My phone is primarily used for work. I need to change my Verizon phone number and get a new Google phone number. I am changing my job description so I do not want my old phone numbers out there and I dont want want to broadcast my new phone numbers to the world. Should I get a new google phone number first and then get a new Verizon number, does it matter the order that I do this in?