The most common current shade style is cylindrical.

What color are you painting them?

Drum shades are one suggestion ... quite a few on this site, and you can upload your picture to see how they’d look.

https://www.lampsplus.com/sfp/39F47/?cm_mmc=GOO-SH--NA--NA-_-39F47&sourceid=DFGPD39F47&gclid=EAIaIQobChMIn--ps9un7AIVUIFaBR0ozgGUEAkYASABEgIksvD_BwE

Another option would be something textured.

I like to look to a lamp's base for inspiration. I think because this lamp base is square it could look good with square lampshades in a colored linen weave. Or I'd try a high cylindrical paper shade in black for drama. I have a lampshade person I work with who is always very helpful in getting the scale and shade just right. Here in Atlanta, there are several sources like that who have booths in antique emporiums (the lampshades are NOT antiques). It's not expensive, it's fun to check out different options, and it's great to get their expertise. And don't forget you could add some fun finials too!

Bring home a cylinder and square to test (or bring lamp with you). You also have to decide on color and texture as well and suggest waiting until after lamp is painted.