This is my humble opinion. If you take this car on a decent test drive, and it runs smoothly, rides O.K. over reasonable bumps without mysterious rattles or loss of control, and all the electrical systems are in working order; what more can you ask for? That’s what a car does; gets you from point A to B and back again a hopefully high percentage of times you drive it. Park it somewhere clean for a few minutes to make sure there’s no leaks, smells of fluid, etc. Have the certified mechanic check it as your links mention.
The fear in buying a car like this is that you will drive it for 2 months and then it will suddenly and inexplicably die, never to be revived again and without any logical cause; based solely on the fact that it was “salvage”. I would say the chances of this are the same for any used car you buy assuming it drove well at the outset. (The only difference being the part about no warranty, maybe.)

Now I’m assuming your family has a “good” car in which to take longer trips in and safely transport that new baby around. Just having something to get back and forth to work in is no reason to waste a lot of money on a new car unless your work requires a certain “status” to be displayed. But then again I’m somewhat extreme in my views on this subject.
I don’t know how reputable the dealer you are using is. Make sure the VIN number on the CarFax report is the same as the actual car you are looking at, and the date is current. You can research the CarFax yourself a little without paying for it. By typing the VIN number into the website, it will usually give you the number of items called out on the car without telling you what they are. If this number matches what the dealer has, it’s just one more indication of legitimacy.
If this car was hit in the back I would pay special attention to the gas tank/fuel area on this vehicle.