I can't answer the transport bit from PA. I bought mine in MD, and it came with paper tags like a new cart would have. Then I got vanity Trailer plates (trailer plates can be annual or permanent. I got permanent vanity plates, can't recall what they cost.) Here's a link to the Trailer registration site.
"Trailers — Permanent plates are available for all trailers (except travel trailers), regardless of weight, for a one-time fee. No additional registration fees will be required for the life of the registration. Personalized license plates are available for an additional one-time fee of $10.00 for permanent trailer plates. Permanent trailer plates are not transferable or refundable."
When we bought one for a boat trailer last year, I think it cost $130, which was a bit higher than when we bought our horse trailer plates 12 years ago.
I have no idea about interstate transport, but when we bought our used boat trailer, we just picked up a $4 "Farm Use Only" plastic tag at Tractor Supply and used that to bring it home. Sure, it wasn't 100% legal considering the DMV regs concerning use of Farm tags, but it worked for us for that one-time trip.
DMV may offer a temporary transport tag, but I don't know if you'd have to get it from VA or PA.
If the trailer currently has an up-to-date tag on it, maybe the seller would let you use it to get it home. Then you would just mail the tag back to him/her afterwards. But don't count on that. When we sold the boat trailer, we gave the Farm Use tag to the buyer to get it home.
Just wanted to add that the $130 for the trailer plate we paid may have included VA sales tax (yep, DMV will get you for that when you go to register the trailer for VA tags). Not sure, though, as I can't remember exactly what we paid total.