This Packard is well within your budget:
http://www.amazon.co.uk/Packard-Bell-Ea ... uctDetailsIt has no touch screen and you can turn of UEFI secure boot and install Linux (you have a second to hit F2 during boot).
If you go to a store you might want to test that Bios setup by disabling secure boot and run a Linux Live CD.
A good sales person will let you do that - a bad sales person will not, and insist that Windows 8 is great, so you do not need to do that.
(In which case he will obviously not be selling anything to you

)
The F keys are strange though, because you have do hold the Fn key to make them work (not during boot, but later).
I do not care to much about that extra "shift" key.
And there are sound keys on the keyboard that may affect the software indicators in your Linux DE.
viewtopic.php?f=22&t=3253I had trouble installing Manjaro on it but Mageia worked.
The screen is good and big enough - that is a pluss.
Not the greatest but cheep - and can be made to work.
Acer might be a better choice. I have no Lenovo experience.