Playing minecraft on an intel hd 4000 at 1920x1080 gave me an average of 40 fps with a 3rd gen i7. If you got one of the computers you talked about at best buy, ask a worker if the desktop would support a gpu such as the gtx 650 and has the 6-pin power connector for it. Then buy a gtx 650 online (it's around 110 bucks), or a similar card, and throw it in there.

Like streetwalker said, you are much better off just building a cheap rig, and can easily make it around $500.
To play those games and many more, this is an example build:
CPU: almost any modern amd or intel (I have a media center with a $120 core i3 that runs anything I throw at it)
GPU: a 100-130 dollar card would easily run all those games and more
PSU: a 550-650W power supply would be more than enough if you are running a mid range gpu
RAM: 4 gigs is enough for playing games like that
Then you can find a cheap mobo that works with the cpu, gpu, and psu, get a hard drive and dvd drive, and a cheap case for about 30 bucks.  Again, this can all be built for around $500.  Gaming rigs that are prebuilt usually start at around 750 if they have a decent gpu in them.