This is good question,well infact there is a LOT..and i mean a lot of redstone kinds,The most used is just like..

Compicated redstonic devices like an calculator/super cannon.

Simple & basic redstonic devices like 4x4 piston doors/Door off/on switch

Compact redstonic deviced like Triple OR quad extenders and contracters/Elev's

Most people use command block for quick-teleportation by activating it with redstone or using pistons.

What do u want to make with redstone?i can help with idea's and tricks for decreasing the size,say whatever u want to build.