I know there are many different satellites, but why would they put a satalite in a geosynchronous orbit vs a low earth orbit? What are the benefits or disadvantages of each?
It depends on the mission your satellite needs to perform. The orbit is something like "where" your satellite is, after all. So what it needs to do dictates its orbit.
A geosynchronous or geostationary orbit will keep the satellite in the same general area. This is useful for communications and weather satellites.
Sun-synchronous orbits have the satellite pass over parts of the ground at repetitive solar times, helping with e.g. ecological observations.
Lunar orbits are useful if you want to go to the moon.
Low-earth orbits are quick, and useful for things that essentially just need to be in orbit but not much else (since they require less energy to get to).