Well, a space elevator is a good idea, but it would need to be incredibly strong. Might be able to make it out of carbon nanotubes, but chances are you would need something even stronger because of the stress caused by the 1000 miles per hour orbital speed of the earth, atmospheric drag, and so forth.
Most satellites use the orbital rotation of the earth to provide a savings in rocket fuel, so they're shot towards the West. Spy satellites are often placed in a North-South polar orbit so they can photograph every square foot of the earth's.
The height of the orbit often depends on what the satellite will be doing. Communication satellites have to be put into a geosynchronous orbit at 22,236 miles above the equator. There's no way around that without having to use multiple satellites like Sirius XM and fancy satellite tracking systems.