Panty requirements vary based on the fit of your gown and your overall desire for comfort.
Thongs work for any bride wearing a fitted gown, but be sure to shop around to find one that's comfortable, functional and an appropriate color. If you're wearing a thin or slinky gown that's just one layer of fabric, you might risk giving away hot pink or even black undies. A color that's close to your flesh tone is less noticeable than white or ivory.
What about those dreaded panty lines? Mermaid, trumpet, sheath and fit-and-flare brides, we're looking at you again. You've got two areas to eyeball: where the panty meets your thighs/buttocks, and where the panty meets your waist. Too-tight undies cause unsightly lumps and bulges, so choose a seamless panty. There are plenty of materials to choose from, so if prettiness is a factor, go for lace. If you're only concerned about function, choose a breathable, unpatterned panty.
If you're wearing a ball gown, A-line dress or something with an empire waist, you've got a lot more freedom when it comes to picking panties. Nothing's going to show through your skirt, so panty lines, fabric and color shouldn't be causes for concern.