some vaios are problematic yes.
however in this case it depends on components. but from this basic data (dual core, 2 GB ram) all versions will run fast on such a mashcine. as long as GPU is supported. sicne it's a notebook the OP will need to test wi-fi, function keys, touchpad, DVD drive if any, hibernate/suspend, battery usage... many things that can go wrong with laptoip compatibility. i too suggest LTS. Ubuntu for it's gnome keep it simple&hide the settings to not overwhelm the user principle and Kubuntu as it works and feels similar than windows. however all other other variants are good and easy to use. so if the user would prefer a different one just install the desktop they want.