How to achieve IQ like this?

I am considering upgrading from a small-sensor camp and not sure which way to go. My primary reason is to improve IQ and I have some specific goals (or dreams maybe) in mind. Ideally, I would like to be able to achieve similar IQ as in examples under this link:

http://forums.dpreview.com/forums/read.asp?forum=1041&message=33171793

I am not sure how properly describe the feel I am getting but it has something to do with extreme cleanliness and richness of the images, being smooth and sharp at the same time, the colors are very natural and relaxing without artificial/digital look.

I am wondering what would be the absolute minimum amount to spend on a system that would be capable of producing VERY similar IQ? Is it only achievable with the highest grade DSLR and lenses that would cost at least $5,000-10,000+? Os is there any budget option that would be close enough to give the same feel? And more specifically, is there any setup under $2,000 that would give (again) VERY close look?

So far, I found these examples from m4/3 to be the closest.
http://forums.dpreview.com/forums/read.asp?forum=1041&message=41582491

There is just a bit of "roughness" in those images and I am wondering if any other system would be even better than that considering that I can get OM-D + Summilux 1.4 for under $2,000. There are so many models and systems nowadays that it is really difficult to track absolutely everything in order to make a long-term decision. Other than IQ, I do need speed and accurate AF as my primary subject will be my kids. I am not sure whether OM-D would be the best choice for that. Anyways, hope some experienced members can help me to narrow my choices (if there are any) in order to achieve the IQ that I like for about $2,000. I am not a brand loyalist therefore wasn't sure which forum is the best for this kind of questions.