CI for MySQL PHP migration project?

As far as the database tables just make sure that you have indexes for all of the search fields.
I would do this with the up coming CI 4 which is more up to date then CI 3.
Check out the CI 4 migrations.

Thanks for the hints!

MySQL is not going to be any faster than Postgres. Why trouble yourself with converting it?

Because it is much easier and cheaper to get MySQL shared hosting than PostgreSQL. Most providers offer MySQL DBs from 1€ per month. Moreover, the DB is gonna be redesigned, so a conversion can't be done anyways.