logging out of old Apple ID into new one
Anything purchased under the existing ID will remain on the device but as you note, you will have to switch logins to update those apps. Whether the hassle is worth it is something only you can answer. Obviously for free apps, you probably want to download them with the new ID.

Music will remain and since there are no updates, you don't need to remain logged in to that account.

When/if you upgrade to a new device, you will be prompted for the username and password that was used to purchase songs (videos, books, apps) in order to authorize the new device to play/use them.

As a side note, if you set up a new Apple ID because your email address changed, in the future, don't do that. Simply login at appleid.apple.com and you can change the email address associated with your account, which also changes the username. For the vast majority of people, one Apple ID is all you will ever need.