What's the right price to pay? As cheap as possible? Kind of a subjective question. Personally I'd go for the cheapo, if I already had a decent flash like the 580. In fact, that's exactly what I did when I had just a 580. But many would argue that you should get a 600. You're really worrying about resale value of a $40 flash?
I don't know much about Newer, but Yongnuo has a variety of flashes from full manual no zoom, to their 580 knockoff. Choose the features you want and grab one. I have one of the ultra basic models, I usually just use it to light backgrounds or as a hair light (snooted). It works fine, it cost me next to nothing, and if I need more features I just use one of my other flashes.
Also a personal preference, but with something as sedentary as an infant I'd definitely be shooting manual anyway.
In the mean time: with a subject as small, and as stationary as an infant you should be able to use a reflector quite successfully for fill light.