How do the speeds at which we are moving with Earth's rotation and orbit compare to the speeds of more familiar objects?

The speed of the rotation of the Earth is, at the equator, about 1040 miles per hour. It decreases as you go north or south, and you can approximate this speed as Cosine(Latitude)*1040. Basically, if you fly a passenger jet from New York to San Francisco, you're just about standing still while the Earth turns beneath you.

The Earth moving in its orbit goes about 67,000 miles per hour; a little faster in January at perihelion, and a little slower in July, at aphelion.