IIRC the oil change interval for most Nissans of that era (My GF drives an '05 Sentra) is 3750 miles. If you "should have done it 6000 miles ago," then you're 10K miles from your last oil change? Ick. If you want this car to last, you really need to be treating it better than that. As others have said, the best thing you can do to make your car last is to take care of all the maintenance on schedule.

Synthetic oil is necessary in some cars (and in fact mandated by their manufacturers, in many cases), but when it's not required, it's basically just an extra expense. My Audi, for example, needs it in order to keep its turbo happy, but my GF's Sentra does not, and so my car gets the expensive oil every 5K miles and hers gets the regular stuff every 3750, but both of them get it on the proper schedule.