Main thing is you don't want to rush into a decision and end up paying taxes out the ears.

@Rob Roy Making sure your VA loan is utilized, puts the cart ahead of the horse.

Ideally, the next tenant will also want to stay for a long time, but if you have a shorter tenancy you can show the nice pics and list it and get a head start on filling future vacancies.

I can't decide whether I should just go ahead and find an apartment to rent out in Greenville and then begin purchasing investment properties.  

That doesn't mean rush into buying things, but start learning everything you can.  

(Numbers for example purposes only.)There's no guarantee your investments will outperform your mortgage, of course, but given the relatively long life of a mortgage the odds of coming out ahead are quite good.Some people prefer the guaranteed 4% ROI by paying down the debt.

So you have to just plan ahead as best you can, be clear with all parties involved about the transaction and expectations, and work in good faith.Tenants will be responsible for all maintenance, care, and cleaning of the property so that everything is in good working order. 

If you're just trying to have the properties all paid off free and clear before you jump into the next one then go ahead and pay it off if it makes you feel more comfortable.

Right now, I am mainly looking for a buy and hold rental property in the Charlotte and surrounding areas.I appreciate the recommendations ahead of time!

You need to know what you're getting into ahead of time before you make such a move.