need new external drive for backups for my older macbook pro (2013) running Big Sur - is there a best out there?

For backups, regular 7200 rpm spinning drives are fine since TM works in the background, so there is no need for an SSD. Personally, I prefer the drives from OWC - they come in several options and sizes:

https://eshop.macsales.com/shop/external-storage

I like the OWC Mercury Elite Pro and Minis (currently have a total of 5 plus some others).

I like to use multiple "bare drives" connected through a reusable interface. Best Buy sells this (https://www.bestbuy.com/site/startech-com-0-15-adapter-cable-for-2-5-sata-drives-usb-c-to-sata-black/5705561.p?skuId=5705561), but there are also "enclosures" from reputable companies like OWC (macsales.com) ... here is an OWC model (https://eshop.macsales.com/item/OWC/MOTGS3U3/). This allows many different backups without buying new connection hardware. Some keep 6 backup drives (TM and clones, 3 copies of each). I will not argue with their success with so many drives, but a reusable external connector allows you to choose how many drives and which types are used even if just 2 backup drives. OWC also sells drives.

Any usb drive will work. I would select a SSD over a HD for reliability and speed.