Make sure your bike has threaded eyelets at the top of the seat-stays and at the bottom near the rear axle.
If you have a rear disc brake, the eyelets may be obstructed and you will need a special disc style of rack.
If you have eyelets, you need a standard bolt-on rear rack. These used to be fairly standard but modern design means that many have compatibility issues with particular pannier bags.
Features to look for include:
3 legs
One set of legs angled inwards for triangulation
An open frame top
Clear space to hook the locking style of pannier mounts: these need a single circular rod or tube of metal (diameter doesnt matter, they come with spacers) BUT they wont fit onto two rods welded alongside each other. You need the rod or tube with clear sections free of cross bracing, tabs or other obstructions.
The top can be a solid plate or open framework. i prefer open style.
At the rear is the ideal location for a lighting bracket.
Some racks feature special rails to fit their bags only. I prefer more standard mounting styles.

Pannier bags need to be
-made of tough material with good stiffening,
-a modern, locking, quick-release mount (not hook and elastic, velcro )
- Heel cutout profile. A rectangular bag may have the mounting rail tilted for heel clearance.
They come in zip, flap or rolltop styles. Zips eventually break, Flaptops can be overloaded, rolltops are the most waterproof.
Some people like lots of organiser pouches, I prefer one main compartment and one external pocket.