Long time lurker, first time poster. 
Ok, bit of a dilemma here. I am planning a new build, mainly this will be used for Mame/emulation using the Hyperspin front end. I also plan to use it for some video encoding etc. and possibly some light PC gaming.
My wife won’t tolerate a “real” PC in the living room where I plan to place the PC connected to a 1080p 46” TV.
As such, I have decided to build a sort of HTPC type build, I am fairly settled on the Silverstone Grandia GD04 as this fits nicely in my current TV/entertainment unit and matches the rest of the aesthetics.
Given I probably wont be doing any heavy gaming, I probably don’t need an uber i7 monster (and budget wont allow).
Problem is I cannot seem to put anything together on a decent budget, I have 2 potential builds, 1 using the AMD A10 and dual graphics or an i3 and a 7850 or something.
The AMD build comes in at ~£800 minus peripherals and the Intel build at ~£900.
I am sure I am doing something wrong and it should be a lot cheaper, but not sure if/where to cut corners.
I want something as silent as possible and something I can probably add a decent graphics card to and play “proper” games at a later date.
Any thoughts/comments/advice would be much appreciated.
Specs below >>>

Ok, bit of a dilemma here. I am planning a new build, mainly this will be used for Mame/emulation using the Hyperspin front end. I also plan to use it for some video encoding etc. and possibly some light PC gaming.
My wife won’t tolerate a “real” PC in the living room where I plan to place the PC connected to a 1080p 46” TV.
As such, I have decided to build a sort of HTPC type build, I am fairly settled on the Silverstone Grandia GD04 as this fits nicely in my current TV/entertainment unit and matches the rest of the aesthetics.
Given I probably wont be doing any heavy gaming, I probably don’t need an uber i7 monster (and budget wont allow).
Problem is I cannot seem to put anything together on a decent budget, I have 2 potential builds, 1 using the AMD A10 and dual graphics or an i3 and a 7850 or something.
The AMD build comes in at ~£800 minus peripherals and the Intel build at ~£900.
I am sure I am doing something wrong and it should be a lot cheaper, but not sure if/where to cut corners.
I want something as silent as possible and something I can probably add a decent graphics card to and play “proper” games at a later date.
Any thoughts/comments/advice would be much appreciated.
Specs below >>>