Leylandii are greedy trees so once the stumps have gone dig in a trailerload or three of well rotted farmyard manure. Digging over the area will also allow winter rains to penetrate the soil, as it will be very dry where the trees have been. You can then plant your hedge anytime this winter as long as the ground isn't frozen.
Don't make the mistake of buying plants that are too big. They will get rocked about in the winter winds and then water will get in around the roots and freeze and the roots may suffer rot damage. Smaller plants will suffer less from wind damage and the roots will establish better in the spring as they don't have a big area of leaves to support. They won't put on a lot of top growth in the first year as the roots will be establishing, but the following year they'll begin to grow away nicely.
A top dressing of fish, blood and bone in the spring will be good for them, and mulching with something that will help retain moisture around the roots through the summer will be good - more well rotted FYM, compost or leaf mould will be fine but keep the area immediately around the stems clear.
Oh, and don't forget to keep the bottom of the hedge clear of weeds and grass - it's amazing the difference it makes to the rate of growth of the hedge.
Good luck - that's a big job you've got on - hope there's someone around to help