Welcome to the hobby! You're off to a potentially painful start going
about it this way in my opinion. Look back at the game posts...
For every person that says a game is great, there is a person who says
it stinks. You need to determine which games you like and go from
there.
Some people love working on pins, some hate it or are just not
technically capable of doing so. You didn't really get into that and
it has huge implications on your budget.
I was fortunate enough that one of my favorite games is Pinbot, which
is still affordable. It has a few issues, but was playable, and the
price was great. For that, I'm able to improve it as I enjoy it.
Here is what I suggest on your budget. Figure out what game you like
in the single game under 2k price range and buy a nice working example
of that game... You can get a near perfect System 11 game and still
have a little money to work with, or you can probably look for one of
the more highly regarded but affordable DMD games like Shadow.
Prices on even the affordable DMD games are all over the map, so arm
yourself with some info before shopping.
Tim