How to sell products for a fixed price (not discounted) with conditions

We are wanting to add a promotion for specific Categories (all Products within the Category which are at different prices) to sell at £1 (with conditions). This is for NEW customers only and can only be used ONCE and on ONE product only (ie. they will only get one item for £1 once). Free shipping is also to be applied. They can also add other items to the cart at the regular price. Does anyone know of a plugin that can do this?
We are wanting to run a promotion for our new business and attract new customers to try us for £1 (we sell lunches). The full price items range between £2.50 and £5.00. Our promotion flyer would say ‘Try a Lunch for £1’.
Thanks