Lugermeister,
My advice, offered entirely FWIW.
Drop your budget for your first Luger to a max of $1200. If you spend 2,000 + USD on your first Luger a time will likely come that you will bitterly regret it.
Buy a shooter as your first Luger and a collector quality gun later, after you have more market experience.
Avoid Guns International, Guns America, Simpsons, and concentrate on the sites like Gun Broker. Spend a lot of time querying and reviewing closed auctions where Lugers that interest you have actually sold. That will educate you on the difference between asking price and selling price, and provide a good idea of what people are actually paying.
Lastly, here are a couple of Luger to look over:
http://www.gunbroker.com/item/708280359
That's an East German refurbished Third Reich era Luger. Contrary to the seller's description, it is not DDR police marked and is unlikely that it was ever a VoPo gun. My sense is it came out of the DDR either shortly after the Reunification (in which case it will be import marked) or is a personal bring back from some trouble spot (in which case it likely will not be import marked). Note the two matching magazines. These will be DDR magazines.
http://www.gunbroker.com/item/711043940
Imperial Erfurt Luger. May be original but looking at the pictures I get the sense it's either a restoration or a 1920s - 1930s rebuild. In either case it's likely to be a good shooter and may actually be a collector grade gun.
If you can get either of those guns for $1000 or less you will have grounds to do a victory lap around the coffee table.
And yes, I'm thinking of bidding on both :-)