external storage for my mac pro late 2013

Yes, a TB3 will work with the 2013 Mac Pro.

I have two Akitio 4-Bay (TB3) enclosures and one LaCie 2TB TB3 External SSD. I connected them to my 2013 MacPro via the TB3 (USB-C) to TB 2 Adapter. Yes, $49.00, but I have never once experienced a problem and I've been using the Akitio enclosures since 2017. I purchased them in preparation for the next Mac Pro. Best of luck for you.

Not without a US$50 adapter.

Use a USB 3 drive -- NOT USB-C connectors, a USB-A shared connector -- no adapters needed.