Simply put here are the basic differences:
Super Automatic Machine which are the easiest to use, have the lowest learning curve, but are also the most expensive type of machine. These machines do all the work with the press of a button - grind, dose, tamp, brew and eject the used grinds.
Fully Automatic Espresso Machines need only press an on/off switch once and the espresso maker will automatically control the volume of water that is dispensed through the coffee grounds and when the pre-determined amount of espresso is brewed, the espresso maker will stop on its own. Unlike the Super Automatic, users first grind their chosen coffee properly and also tamp the coffee properly so it fits correctly into the portafilter. Next, the portafilter needs to be attached to the espresso machine and the on/off switch pressed. Because of the pricing this is mostly used in commercial settings.
Semi Automatic Espresso Machines are the most popular style chosen for home use because they produce an excellent product and automate a lot of thing for you but still give control over how your shot of espresso will progress. Unlike the Fully Automatic, aside for pressing the on/off switch to begin, once the desired espresso is extracted from the machine the switch needs to be turned off; thereby controlling how much water is released.
Manual Espresso Machines which are traditional style machines are recommended for true coffee aficionados and those who truly enjoy the process and effort involved in making a cup of espresso. This machine is piston-driven and requires the operator of the machine to pump the lever to pressurize the hot water and send it over the coffee grounds to pull the shot. Manual espresso machines are totally dependent on the user focusing on the pull of the lever.
As a newbie, the Semi would be your best choice for your first espresso machine, not too expensive and fairly simple to use. The Gaggia Classic is a great choice- very popular because of its many great features. Make sure you budget as well for a good grinder. Good Luck!