Choose which ever has a proven and supported Ubuntu graphic card support, since that is the hardest to get/fix/make it work
http://www.notebookcheck.net list all graphic cards for laptops in order just type in the name of a card any card and you can just look to the right and see each card in order and under each card what score they got
So far the best card made for a laptop is the 280M Nvidia card
The ASUS G Series G51J-A1 does indeed have a nice graphic card the GTX 260 M
Indeed that computer is very good and could even be a good gaming computer if you hook up a nice monitor, a real keyboard and a real mouse.
And it is way cheaper than number 2
The HP ENVY 15-1050CA does indeed have the second best card and is 500 dollars more expensive and the extra 2 gigs vs a better card I would go for number 1
The third the HP Pavilion DV7-3080CA cost the same as the first but with a worse card.
For me as a person who likes games I would of course go with number 1 and then again I wouldn't upgrade that machine to Ubuntu but keep the windows 7 and play lots of games.
The question is what do you want to do with the laptop just work and nothing more or play games as well.
It all depends what do you want to do?
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