Don't match your suit, tie or shirt (matching a secondary colour on the tie is often a good option, but even then you don't want them to match too closely).
Cotton, linen or wool squares are more casual. Silk is a bit more dressy. Linen goes with everything.
I'm a big fan of all Kent Wang products, including cuff links. They're all nice. Plain shirt > more flashy cufflinks. Patterned shirt > plain cufflinks IMO.