Given that the major part of the cost here is the CPU then the 'k' chip should only be slighty more expensive at build time so I would specify that at least as it will give you more options for upgrading other components further down the line.
Likewise a low end z77 board shouldn't be that much of a hike over the one he defaults with.
So for something like £60 over what he's asking for the base machine you should end up with a decent basis to start to work from.
What ever route you take you will be able to add a better video card than the on-chip intel graphics which work fine for running X1 @ 1080p.
Ask for it to be left at stock speeds because the only option he has on the locked chip is to increase the base clock rate which opens up issues with memory timings i.e. possible stability problems if it's not done right. Any performance gained from messing with that is only marginal anyway. At least you know if you start out at stock speeds any problems you run in to you will have caused yourself.
I went the budget route also with my current machine and it works fine for my needs and although I have the 'k' version of my sandybridge chip it's the H67 based motherboard that keeps me locked down speed wise.
Having said that I get plenty enough from it for my current needs and it's certainly no slouch for my performance requirement.