You’re buying a house with security devices
A new home may come with an installed home security system. All the devices function well, are placed in the correct places, and are ready to go. In this case, just get the phone to call and establish a new monitoring contract. A Vivint installer will still show up to make sure there are no integration issues, and they might offer ideas on an upgrade or two. It's a quick appointment, and you can have your monitoring set up without worrying about any new devices -- unless you make additions.
The outgoing owners can give an existing Vivint contract to you for a one-time set-up fee to make your life simpler. If the outgoing residents are downsizing to an apartment complex or retirement community, transferring the home security service might be an addendum of the sale.
You need to move and bring your existing equipment with you
You may want to bring your favorite home security components with you to your new house when you move. It should be pretty easy to transfer, as modern smart devices are plug and play. You can take down each device yourself or use a professional installer to come and take care of your devices. Then a pro will put in the same devices -- and any smart devices you want to add -- in the new place. Your home security contract will keep the same.