I would avoid concrete for several reasons. It's hard and cold and doesn't drain, so even if the run has a roof there will always be damp patches in wet weather where rain blows in sideways. Concreting that quite large area would be hard work, given that you'd have to dig it out first and then mix it. You would end up with a big slab of concrete in your garden, which would be there forever whether or not you (or a future purchaser of your house) still wanted to keep chickens on it. If you really wanted hard standing to prevent vermin from below, concrete slabs on a bed of sand would be easier to put in and could be removed if you changed your mind.
When we built my run, we laid 1/2" galvanised mesh over the whole floor area and wired this about 15-20cms up the sides all round. On top of this we laid permeable weed proofing membrane to protect the chickens' feet from the mesh and to give good drainage. Then I added a good layer of Aubiose (shredded hemp, sold as horse bedding, extremely absorbent, easy to poo pick, warm and soft for the hens to walk on and they love scratching in it.) Seven years later, the first lot of membrane was still intact this Spring, when I had a complete clean-up of the run before getting a new generation of chickens, and I replaced it with a clean new sheet for less than £15. Whilst the run was empty of hens, I left a pot of corn out, which was untouched for several days although I knew there were rats under a neighbour's shed next to the run, so the mesh was still working well.
You do need to get lots of metal tent pegs to fix the mesh down flat, unless your run floor is perfectly flat, which ours wasn't. Also plenty more metal pegs to fasten the membrane down round the sides and into the corners; plastic fixing pegs won't go through the 1/2" mesh underneath. These are available quite cheaply on Ebay, as is wide membrane which will go right across the run in one piece. For a 12ft run, get a piece 4 metres by 5 metres, to allow for folding under the ends to prevent fraying when they scratch around.
A lot of us have found that Aubiose is better than shavings, being much more absorbent. If you can find a local stockist from this list,
http://www.aubiose.co.uk/stockists.php you might be able to avoid high carriage charges by collecting a couple of bales in a car when needed. Two or three bales would start you off with a nice thick layer on the floor and a spare one for topping up as it gets removed when you pick up poo. It's good in the nestboxes and coop as well.