Sounds like a nice find!
I would begin by verifying that there are no trouble codes present. If there are no codes, you should start replacing the maintenance items, such as the air and fuel filters. And thoroughly inspect under the hood for any evidence of rodent damage. (ie chewed wires, vacuum hoses, etc.)
If the problem persists after doing the routine maintenance, probably a fuel pressure test is in order. I would focus on the fuel system first, due to the low mileage, and the age of the vehicle. A lot of condensation can collect in the fuel tank of a car that is only driven 1000 miles per year! Hopefully, your problem is just due to a semi-water clogged fuel filter.
How does the car run otherwise? Does it idle smoothly? And does the engine pull hard all of the way to red line?