Need new photo-editing, Photoshop no longer compatible. Help!

It appears you were using an older 32 bit version of Photoshop prior to upgrading the Catalina. There is no "best" replacement of any application, if you want to replace something you have to find something that suits what your particular needs are. As we would have no idea how you use Photoshop then I'd strongly recommend that you research Adobe's updated version of Photoshop that works in Catalina.

Please navigate to www.adobe.com to begin your research.

You might consider the non-subscription, Affinity Photo, which works fine on Catalina. It can open and export Photoshop .psd files, and ultimately, you will have to decide if it complements your PhotoShop replacement requirements. There is a free trial from the vendor's website, (scroll to the bottom of that webpage for the free trial link) and it is also in the Mac App Store. Affinity Photo is on sale right now for $39.99USD.

The Affinity applications were all designed to work together from the same document format, where Affinity Designer would be the replacement for Illustrator, and Publisher would be the replacement for InDesign.