You cannot legally purchase a firearm in person in a state you are not a resident of. It would have to be shipped to your home state where an FFL holder would complete the background check. Then there is the separate issue of transporting across state lines to shoot at a range where you don’t live. There are many regulations you need to look up with the ATF.
Regarding everything with the purchase all you have to do is stop in. I don't know what's involved in the interstate sale it might not be possible depending on New Jersey laws and Pennsylvania laws. I think the annual membership is either 360 or $400 and that get you unlimited range time and some discounts especially on rentals. 20 Lanes rarely a wait
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