How can I prevent all of my old deleted emails and read emails transferred to my new phone?

When you transfer data to a new phone NO emails are transferred, because emails sync to a mail server, not from device to device. So if you log into the same email account on the new phone that you had on the old phone then you will get exactly the same emails in the same folders that you had on the old phone. You can edit the folders on either the old or new phone and delete emails you don’t want to keep, and you changes will be reflected on both devices, as well as on the mail server and the mail provider’s webmail page.

Well, the general instructions are in this support document→Transfer data from your previous iOS or iPadOS device to your new iPhone or iPad - Apple Support.

However, that will not transfer email content, contacts, calendars, reminders or notes, because these items sync to your email provider's server or servers if you have more than one email account. You get them back by logging in to the same email accounts.

when you get a new iPhone you can set it up from a new iPhone and with iOS 11 or later a little pop up on your iPhone asking if you want to setup the new iphone

Try using Apple iCloud by backing up your files from your old device and logging in to iCloud on the new phone.

Here's a guide by Apple that may help: How to back up your iPhone or iPad with iCloud - Apple Support

Questions? Let me know and I can help.

Sorry apples_aregreat, but your post has absolutely nothing to do with the original question, and nothing to do with NOT transferring email. You aren’t the only one that misinterpreted what SuperStew posted, however.