If you're willing to learn and enjoy the journey and rewards of getting your hands dirty, and maybe have a little luck, you can get some great games for well under $1500:
- In October 2014 I bought my first pin for $550: a Space Shuttle with nonfunctional pop bumpers and flippers plus the usual wear and tear. I knew NOTHING about pinball machines but had a few things in my favor: being technically inclined (to handle all aspects of repair), having some artistic ability (to touch up and clear the playfield), and finding PINSIDE to learn all the nuances and particulars. I documented it in a restore thread here and got lots of help and encouragement from a community I'd never heard of before. So even after paying to get some board service done, I finished the machine to near-new status for under $1K, and made it nicer to boot. My first game is now a rock solid awesome fun machine, trouble-free through almost 3000 plays, with plenty of accolades and fanfare from its first show outing to boot.
- In May 2015 I bought a wrecked Firepower project for $300 and in some respects I probably paid too much even then. I would NOT recommend buying a basket case like this! Even so, nobody will say Firepower is a bad game and you can find turnkey playable examples for under $1K, to a little more for a nicer one. I'm probably into mine for that $1K figure but it's far nicer now than any I've seen sold for that price.
- March 2016, I fell in love with Space Station at a show. Of two examples there, one needed TLC but never missed a beat during the entirety of a 3-day show, so I knew it was solid. Managed to find the owner and brought it home for an even $1K. A hundred or so in standard shopping (flipper & pop rebuilds, new rubbers, misc repairs, etc) and I'm still well under the typical price for that one, and it's a fantastic game.
Of course it goes without saying these are not DMD games. But honestly, I can't say a DMD itself makes a game great. Some DMD games are generally considered "bad" while some SS (and even EM!) games are still desirable today. Firepower is an all-time classic that's worth cutting your teeth on. Space Shuttle saved the whole damn industry and when you play it you'll see why. Space Station is an odd one, but has incredible light shows, great sound for its era, ramps, diverters, multiball, hurryup, jackpot, a non-standard layout... pretty much all the things DMDs have except the screen.
So as others have said, don't fixate yourself on any one title or group of titles. Get the Pinball Arcade app, and play as many as you can to see if you like the rules and sounds. Watch PAPA vids on YouTube. Go to locations and shows. Consider getting your hands dirty as that will save you some money up front and hopefully forge an appreciation for these fantastic, wonderful contraptions Either way you'll either find something you love for under $1500, or something worth saving a little more for. The options are endless.
Also, you should start saving for your second. It WILL happen.