To get P3D to run as well as possible, you need same specs for the computer as for FSX. Of course everything depends on the addons you are going to use and using only default P3D isn't that big of a problem, but when you start to add complex planes, AI traffic, heavy scenery and HD texutres, you can literally bring down on its knees every single normal desktop PC there is available even with top of the line hardware costing thusands of bucks. So, limitations are also the same, and the software is really CPU bound because of the poor multithreading. Many FSX tweaks are also usable for P3D, some aren't needed anymore. P3D still works, at least for me, a lot better than FSX.
If upgrading solely for P3D, I'd probably go with Intel 3550K or 3770K, get good enough cooling so I could take the CPU to or over 4.5GHz. P3D is 32-bit program, so it can't utilize VAS more than 4GB, but of course other programs in the backround use memory also. Memory is cheap, so at least 8GB and that should do just fine. SSDs are also getting quite cheap, so I'd consider perhaps one ~250GB SSD for it, depending on the amount of addons. SSD mainly shortens the loading times. With the CPU, graphics card is the most important component. If on tight budget, you could find for a fairly cheap price GTX480, 570 or 580 card, which are still good for P3D/FSX. If looking for a new card, then I'd go with GTX660ti at minimum all the way to new Geforce Titan, which is 1000 bucks, but the best you can get for P3D now.