What is the best cost effective option for an external drive for time machine backs for a M2 Macbook Pro with a 8TB hard drive?

Welcome!

First, I confess to putting the "cost-effective option" part in abeyance when I asked myself, "What are my photos and files worth?" I'd suffered with cheap external drives, both mine and those on friends' computers that I support, and finally said "Enough!"

For TM, an SSD is overkill. A USB3 drive enclosure with a quality SATA 6, 7200-rpm mech drive inside is more than fast enough once the initial backup is finished.

For best reliability, I use only self-powered enclosures (they have an independent power supply) that hold desktop-class 3.5-inch mechanical drives. For drives inside, I avoid the entry-level stuff that most drive makers offer to placate the mass merchants. All my TM drives have WD "Black" series drives which have been a good blend of reliability and cost. I use these empty enclosures:

https://eshop.macsales.com/item/OWC/ME3NH7T00/

It takes minutes to install a bare drive in those enclosures.

As for size, the traditional recommendation has been 2-3X the size of the internal drive it backs up. I use 2X. My iMac has a 1TB factory SSD about 60% full and has been backing up to the same drive since 1 April 2019 when I installed new new 2TB external drive. After over four years, it still has its first backup and is under 80% full. That works for me. Your mileage may vary.

The "best" choice is up to you, but two brand name HDDs is my recommendation for adequate data security of that much data.

But with the size drive you have, you're going to be into a little money here. How much is your data worth to you?

Just don't fall into the "Eggs in one basket" trap. With a drive that size, the tendency is to load it up. Just recently on this very community a poster was woefully regretting that decision coupled with no backups.

I use worst case analysis when it comes to backups: Plan for the worst; hope for the best.

Modern drives larger than about 4GB are often assumed to be always running. Because of this, on some models, the electronic brake has been removed.

That sounds fine, until you want to choose Restart off the  menu. Often the drives do not spin down fast enough, and so when the Mac start up again, they show status: not ready, and are not mounted.

The solution is DON'T Restart. Instead, choose Shutdown, count to ten, then start up again.

I commented on the concept of providing good and adequate backups and the dangers of not doing so..

What peripherals you buy is your choice. We all have our favorites; I know nothing about Orico.