Hi. Whether you get a short neck or long neck 4 string banjo, how you tune it is crucial. There is no "one tuning", since you're using it for other than it's original purpose. (Jazz)
4 string banjos are easy to find, and ALWAYS negotiate, cause they sell MUCH slower than 5 stringers. If you're lucky enough to find a Gibson, Vega, Paramount, Orpheum, Slingerland, Epiphone, or other recognised name, still put in a lower offer than they're asking. DON"T buy a new one of ANY kind. The old ones are much better. Good luck.
rick