Hi Sam,
Welcome to the forum.
To answer your question about electric fencing, in addition to the netting, battery and energiser you may find the following useful
http://www.rappa.co.uk/products/145-fence-alert
which flashes a red light if the fence isn't working. I found it invaluable when for some reason I had forgotten to reconnect the fence on leaving the enclosure,
and this
http://www.amazon.co.uk/Farm-Care-Elect ... nce+tester
which tests the fence voltage and will indicate if it' shorting out somewhere or damaged.
One thing I intended to do but didn't get around to was to put a strip of Damp Proof Course material underneath the netting. Closely woven landscape fabric would probably work as well. Provided it doesn't get puddles on it when it rains, it will keep the netting from touching the wet grass and saves the hassle of trying to keep the grass short. It will of course temporarily kill the grass and you may not want the yellowing strips in your garden.
Make sure you have plenty of double pronged poles - they are good to use at corners. My enclosure was more of a circle and I also used guy ropes and pegs at intervals to help hold the 100 metres of netting taut.
On the subject of batteries, you need a Leisure battery, not an ordinary car battery. They are more expensive but are better suited to the job. Remember your protection is only as good as the battery powering it and I think it's possible to get a solar powered trickle charger. Without getting too involved in the technicalities of voltage and current, a normal car battery is designed to give a short high powered burst to start the engine. A Leisure battery is designed to run things like lights, fridge, TV in caravans and motorhomes where constant lower power is required - exactly what you need for your fence.
I had a Gemini 80 energiser which would work with either battery or mains (I was mains powered) and would easily cope with my 100m of netting.
One cautionary note about the house and run. If my maths is correct the run size, including the area under the house is about 6.5 square metres. The recommended minimum space is 2 square metres per hen, and 4 is better. From your post it looks as though you intend to have them out in the electric enclosure, which with 36 metres of netting gives them about 80 square metres in which to scratch about. From what I have read about ex-batts it will take them time to get used to the big outdoors, but too little space and problems such as bullying and feather pecking can occur.
Enjoy your hens and have fun, but make sure your inoculations against "MoreHens" disease are up to date!!
Lost the post before I submitted it so had to re-write and have just seen Dinosaw's - no time to edit this!