With the migration assistance, can you select certain files you want to transfer to the new Mac? I don’t want everything transferred from the old to new.

Migration assistant is pretty much all or nothing with regard to files and folders.

However, all you need to do is create a TM backup having sequestered the unwanted data in a single folder you can later remove and migrate using it.

Or delete the unwanted data and make a new TM backup.

I think either of these would be cleaner than trying to pick and choose TM during migration.