Laptop and a desktop? If they are both going to be doing the same kind of stuff and it's just facebook and the like a mid range laptop will fly through that all day long. If you would rather make use of a bigger screen when at home just connect up to a second TV or monitor.
This spec will last for ages and you could just hook it up to a monitor while at home if that would help. It also have more than enough power to breeze through your intended uses.
Chassis & Display
Voyager: 17.3" Glossy Full HD LED Widescreen (1920x 1080) (£35)