Since it has an 8-track player, the console is almost surely solid state. This helps because any audio device that is vintage and tube based usually needs capacitors replaced and usually has some tubes that are dead or dying. It's a good weekend project if you are handy with a soldering iron, but most people don't want to do that.
That being said, the initial pop you hear from the speakers is due to the amplifier turning on. This is due to there being voltage spike from the amp suddenly drawing current. Most receivers and amplifiers have a relay built in that prevents the amplifier from sending out any signal to the speakers within X amount of time from being turned on. Since the console either doesn't have relay or it has gone bad, you might have to do some electronic surgery to prevent the pop. Without getting too indepth, a manual DPST (or more common DPDT switch) hooked up to the positive wire of each speaker will work. It would mean having to turn on the stereo, wait a few seconds, then flipping the DPST switch, but it would be the most simplistic fix for that problem. Most people who are skilled in electronics could easily do it for you and make it so the cabinet doesn't need to be altered. Whatever you do, never alter the cabinet itself, only the electronics inside if you must.
The static, popping, and sound cutting in and out is most likely due to dirty potentiometers. Usually the volume and balance pots have dirt and dust accumulated in them from years and years of use which causes dead spots. Go to Radio Shack and pick up some contact cleaner. Take off all the knobs on the stereo, spray the contact cleaner in the pots, and turn each knob back and forth for a good 20-30 seconds to work it in. Wait a few hours and turn on the stereo again. This usually helps get rid of those dirty spots that are making trouble.
A more permanent solution is to completely replace the pots on the stereo which is a time consuming job that might alter the sound of the stereo. Some of the pots used by stereo manufacturers degrade over time and no amount of contact cleaner can completely fix them. This means removing the PCB from the stereo, desoldering the old pot, putting in a new pot, and reinstalling the PCB. Financially, it isn't worth it with the majority of stereo consoles unless they are a very rare piece. If the console has some personal value to you then it is definitely worth doing, especially if you plan to keep it for awhile to come.
Audiophile and collector of vintage audio equipment