Yes the PSA upper will work with a Standard AR lower, You will need a couple of Specialized items, (1) Quality Magwell adapter for either Glock or Colt style Magazines, one of the nicest I have seen is from Macon Armory,(2) you will also need a 9mm Buffer, I would suggest that if you use Colt style Magazines, that you get a Buffer spacer (Available from New Frontier Armory or Joe Bob's) to limit Bolt rearward travel and eliminate the possibility of breaking your Bolt stop. Stick with a Milspec lower w/ Milspec Fire control group, No notched hammers or fancy A** spring setups., Carbine length Buffer tube.
The Buffer, Buffer Spring and Buffer Spacer are available from Joe Bob's Outfitters at a reasonable price.
If you decide to go with the Glock Magazine adapter you sacrifice LRBHO (Last round Bolt Hold Open), But Magazines are readily available almost anywhere and all sizes if the 9mm double stack mags work, If you go with a Colt Magazine set up the Magazines become a little more difficult to find, Several companies make them, but Metalform are about the best, PSA sells them for $19.95.
Have fun and shoot straight.