No need to use Google Apps for this. There are several ways to redirect mail.
Launch the mail server, by far the most complex, but it is free and you have full control.
Amazon WorkMail is cheaper than Google Apps, but you still have to pay for it.
Mailgun is a great service and probably the easiest to work with, and it's free if you don't send / receive a lot of mail. Check out this guide to get started: https://renzo.lucioni.xyz/mail-forwarding-with-mailgun/
There are many, many others, too many to list, but I think this is a representative sample.
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