Are you recommending that I do not buy a rebuilt alternator?
If you have a local shop that rebuilds electrical components, they would be your better deal, the shop I use rebuilds the entire alternator for $65, not just replace the worn parts like most "auto parts store" rebuilds are, and if you do buy a rebuild just have it tested before going home.
I did not get an amp with my stereo because I don't have subwoofers yet. If I plan on putting in an amp should I get a high output alternator?
Since it started with the stereo install, asking about the system was to remove something like a high power amp from the cause.
Depending on t he amp draw you may need to go with a bigger alternator, the stock 70amp one should be fine with a single amp up to 400 watts.
And what do you mean by degreased?
As Mudder mentioned steam cleaning it or using the cans of engine cleaner/degreaser that you hose off with water, if you don't cover/remove the alternator, the grease and water will kill it, same with a leaking power steering pump.
The motor is a rebuilt engine with only 1000 miles on the entire thing.
When you put the engine back together, did you put a new fuel filter on, did you have the injectors cleaned?
Okay so I went out there this morning and took it off the battery charger. When I went to start it after it not running for a couple days it runs for a second then shuts down.
What was the result from testing the alternator voltage?
If you don't have a voltage issue, it may be a fuel issue, pump, filter, injectors.
It does this multiple times until it starts to idle correctly. Is this a problem with my cold start?
Cold start issues could be the injector itself, or the cold start timer switch. You can pull the cold start injector and test it on vehicle, remove injector then hook it back up, unplug the coil(so the engine can't fire up), have someone turn the engine over and see what the spray pattern is like from the injector, should have the injector spray into a clear plastic jar or bag. If it fires fine, it is likely the timer, that can be tested with an ohm meter, or firing the injector manually before turning over the(will need to attach positive and negative wires to the injector terminal, and tap the positive lead one the battery to fire the injector.
Other things to look for would be a cracks in the intake hose, loose/cracked vacuum lines, too much unmetered air will make the engine stall out, should also check the distributor, if the set-bolt loosened, the distributor could have moved and the timing is off. The air flow meter or throttle position sensor could also be causing the problem.
Checking for engine codes will help to determine if the problem is mechanical or sensor(not always) related.
Sorry for all the questions I am just trying to solve all the issues I am having so I get a strong running truck instead of it breaking down with a different problem each week.
If I remember correctly it sat for years after you grandfather started to repair it, so having new issues pop up with it back on the road is understandable, especially if you don't know what it was running like before your grandfather started the engine repair. Diagnosing automotive problems is a skill that takes time and patience to learn, the frustration you are dealing with now is the cost of acquiring a skill that most men, including a lot of auto techs no longer have.