Basic Training Graduate usually means: General discharge (not very good) OR General discharge under honorable conditions (still not great, but leaves open the possibility, however small, and it is VERY small, that it can, at some point in the future be appealed and upgraded to an honorable discharge.
If you complete basic training, and swear the oath (you're not actually a member of the armed forces until you do both), and exit the armed forces with anything but an honorable discharge, you have placed a pretty large burden/stain on yourself. Any job application (for a job of any import) is going to include questions about military service, and one of those is going to be: Were you honorably discharged? Lying about that is a criminal act, and if you're truthful (in the case that you did not receive an honorable discharge) then your application is probably going in the waste basket. It's not something you want on your easily verifiable record. And it never goes away.
A dishonorable discharge is the worst of course, but that is likely going to be accompanied by a felony on your record and jail time.