Which model of the SonyA7 series is best for sports photography?  ?

For sports photography you want a high frame rate (i.e. the ability to shoot as many pictures as possible per second), To do so, the camera cannot have too many pixels because if the camera has to handle a lot of pixels, then it will slow down the number of frames it can handle per second. That is why the top cameras Nikon and Canon make for sports have only around 20 megapixels. Fewer pixels also provide the advantage of bigger individual pixels, so that they can collect more light, which is very important since higher shutter speeds would be needed to stop action. The larger pixel means the camera can produce pictures with less noise at high ISO settings in low light situations such as indoor basketball games or outdoors on a cloudy day or at night. The A7 is therefore better than the A7S or A7R for sports. 

You would be best served with a DSLR and not a mirrorless at this time.  Reason being is that a DSLR like the Nikon D850 or the Canon 7D Mark II has a better AF system than a comparably-priced mirrorless.  AFAIK, the only mirrorless cameras that can compete with a DSLR in terms of AF performance is the Sony A9 and the Nikon Z7.

But, if you are dead set on the Sony mirrorless series and since you occasionally print at 17x22, go with the A9 or the A9II, both of which are more than $1,000 above your stated budget.

Personally, I'd go with the Nikon D850 if I had to stay as close to the $2,000 range.

I've not used any of the cameras mentioned, and to be honest, I basing my answer on my understand of the AF performance reported by reviews that I've read or watched and not on personal experience.  So if it were me, I'd rent the bodies that are on my short list one at a time and get an actual real-life understanding of which one is best for me.  Lensrentals.com is one such place to rent gear for a week before you buy.  The cost of the rental will be substantially lower than the depreciation hit you'd take if you ended up having to sell your new camera if it wasn't good enough for your needs.  Of course, anything you buy in the $2,000 price range will be better than the A5100.

Because you print fairly large, you would want to consider at least a 40MP sensor if not higher.  Just be aware that these high-res cameras are typically designed for the landscape shooters and not the sports shooters.

If 17x22 is the largest you print, then you already have all the resolution you need in your current camera. If you think you need full frame (which you don't), look at the new a7c, which is a full frame version of your current camera.