"You get what you pay for."
I guess. Maybe there is more than one way to pay. You can pay with money: "This pistol HAS to be good, because it costs $1,000." I think you can also pay by gaining knowledge/experience instead of (or in addition to) paying with money. Thus the OP was wise to ask advice.
As far as I know, the EAA pistols are still made by Tanfoglio in Italy. Tanfoglio makes fine handguns, including match-grade target pistols. My Tanfoglio CZ clone 9mm pistol is Israeli surplus. It was used for military training or by a military-related pistol club (it's marked "Cohai"). The Israeli military is not known for buying junk equipment. It didn't cost me very much money, but it is a very good pistol. I own or have owned pistols made by Browning, Beretta, Colt, S&W, Sig, CZ, etc. My Tanfoglio shoots as well as any of them, and it's any easy guess that it's also been shot more than any of them, too. Just because I was smart enough to get it inexpensively doesn't mean it's a poor-quality pistol.
The two best recent deals in 9mm pistols were both a couple of years back. There was a big batch of Italian Berettas, and a big batch of Star Super B's. I think my FiL paid around $250 for one of the Berettas. It looked like it hadn't been shot much. I got one of the Star Super B's for something like $230. It had barely been shot. My FiL liked it so much that he immediately ordered one for himself. He found a different place and paid a little less than I did. His was NIB with papers and everything!
If the OP can find one of those Star Super B's, they are excellent pistols. They look like a 1911 with no grip safety, but they are 9mm parabellum and use the locking system of the Browning High Power. If the OP doesn't mind single-action pistols, I would highly recommend them. Mine seems very well-constructed. I don't believe that I will ever wear it out. (Though the Stars admittedly don't meet the magazine caveat.) The Berettas are nice, too. They have the annoying magazine release on the heel thing, but they are good pistols. I still see a few of each every once in a while, and they are well within the OP's price range.
lsudave and I seem to think alike. I also own most of the pistols on his list, and paid about the same for them.
One other thing I just now thought of, CDI Sales on Gunbroker has a bunch of surplus S&W 9mm pistols for sale right now. There are 2-3 different models. IIRC they are about $200-$300 apiece, depending on their condition. I have not owned one, but I have heard good things about them and it sounds like a good deal. My experiences with CDI Sales have been very positive.