You can buy a cheap laptop with an Intel integrated chipset and without
Windows (for instance at LDLC) + a Wifi adapter at
http://libre.thinkpenguin.com (25% of the benefits on your purchase go to the
Trisquel project).
For example :
http://www.ldlc.com/fiche/PB00158586.html
+ https://www.thinkpenguin.com/gnu-linux/penguin-wireless-g-usb-adapter
As it has already been said, you had better take an Intel processor but
without the TXT or vPro "technologies".
As for the Wifi adapter, you can opt for an internal card such as
https://www.thinkpenguin.com/gnu-linux/penguin-wireless-n-half-height-mini-pcie-card
However the USB adapter is particularly useful if you want to carry with you
a Trisquel Live system and get a Wifi connection on the computer you plug it
into. Also, it is kind almost guaranteed that the USB adapter will be usable
with your computer you will buy after this one. Probably the one after that
too.