OP - DM is the best game you mention in your list. But for $3K, you should be able to get BOTH a Data East Simpsons and Hook. As an alternative, perhaps a DM + a cheap EM machine or a beater/project SS to boot.
Personally, DE Simpsons was my first game and it was great... until I got so good at the shots that the shallow rule set and quick ball times got real old. Hook is very similar, but looks nicer IMHO. I don't know what would happen with both of them side by side and if they're able to be kept longer without getting bored.
DM will probably have a lot more replay-ability, but is also much more complex of a game to work on. If you have a good technical aptitude, get a DM. If you want simplicity, get both Simpsons and Hook. If you want the best option for a $3K budget, get out there and play some other games and perhaps find a top tier Bally/Williams game, or a cheaper Stern that will really maximize your budget.