You can get a lot out of a pull-bar as well, to target core and back. Especially if you add some elastic bands. It's also helpful to have a reference like this around, to give you ideas for isolating exercises:
https://www.amazon.com/QuickFit-Suspension-Workout-Exercise-Poster/dp/B07NBFM4LZ
But my biggest recommendation is to hire a trainer for a couple weeks as you get started with this. Lots of trainers are working virtually these days. The thing about both core and back exercises is that you need proper form and to understand how to properly target muscle groups. Especially for lower core exercises -- many people just don't understand how to engage their lower core. You can do all the exercises you want, but if you have improper engagement, you won't get the results you want (and could cause strain or worse). So I'd get a trainer to work with you on form and maybe give you a few different exercise sets to work on for variety.