The 10K machine shop thread seems outdated as the price of the lathe has jumped dramatically and the mill doesn't seem to exist anymore.
I have heard very good things about this lathe
http://www.machinetoolonline.com/PM-1127-VF.html. Supposed to be much higher quality than the average Chinese machine tool.
I have extensive personal experience with that JET lathe and it is trash (and overpriced) in my opinion. The fit and finish is very bad. It's extremely difficult to use, does not easily hold tolerances well, and has almost zero power.
You can get the machine I linked, with DRO, for only $400 more than that JET. Or the base model for less than the JET, while having power feeds on both axes, infinitely variable speed (very nice), longer travel, and much heavier duty.
I would avoid the 2 in 1 machines like the plague. you end up with two poor quality/poor usability machines instead of 1.
I know you asked for a recommendation of a mill in the $2000 range, but I will
throw this out there in the off chance you can afford more.
I've posted about this machine elsewhere. We have it in our trailer that has supported many FRC events in the last 8 years. It is much higher quality than the average benchtop mill. It can take real cuts and the fit and finish is quite good. It's the only small mill I've ever used and not absolutely hated. It is more expensive than you wanted to pay, but you get what you pay for.
You will find a bunch of round column JET and other brand mills in the price range you are looking at. They will all be identical, made in the same factory in China and then rebadged/painted for each brand. They will all be relatively poor quality (though much better than the 2 in 1 you linked).
If you are locked into a budget of $2,000 then you are pretty much stuck in round column territory, unless you want to go with a smaller capacity machine
like this . That's not to say you can't produce good parts with one of those machines, it's just going to be more difficult and less user friendly. I think the extra cost would be well worth it, but if you can't swing it you can't swing it.
As previously mentioned keep tooling in mind. You will likely spend at least 50% of the cost of the machine on workholding, toolholding, cutting tools, etc