I am looking into getting a stereo for my car. I am planning on getting an all sony system (Sony CDX-F7700 deck, two front 4", two back 5.25", and two 12" subs with a 1200W amp). Is this a good system for a good price to install into my 1991 carolla? Sony CDX-F7700
There are a few ways you can determine if your electrical system is capable of handling the equipment. If you are just installing new headunit and speakers, then you won't have to worry about it. However, since you are plan on using an amplifier to power the sub(s), that's where the most power requirement will be at, since it's an older car. Typically, the alternator is only rated for 65-70 amps, since older cars don't have the intrinsicity of newer cars.
The easiest way, longest effort is to install all the equipment and see if your car is capable. Make sure to keep the car running when playing, since the alternator is what keeps the battery fully charged.
The easiest effort, hardest determination is to take all the ratings of the equipment and figure out if the stock system can handle it. You'll need to know how power relates to voltage and current.