Our neighbour took out his diseased leylandi trees which is the boundry between us.

Instead of replacing with trees we have a lovely wooden fence

A fuchsia hedge is nice came across this last week which is very effective .

Chrismas box makes a nice hedge to or lawrel but am sure others on goy will suggest a lot more.

Need more info please - what purpose will the trees serve exactly, and do you mean trees or shrubs? Are you looking for stand alone trees dotted about (in which case, how big is your garden) or for hedging, or privacy. If the latter two, how tall do you need it to get?

What's wrong with the conifers you're removing (this might have implications for replanting)?

Whatever you plant you'll need to do a lot of soil improvement first as the conifers will have taken all the goodness from the ground. Dig in as much good compost
as you can. If you haven't got much try a mulch of chopped fallen leaves and/or grass mowings left on over the winter. If you don 't do this any planting is likely to disappoint you.
How high do you want the new hedge to be? Remember that anything reasonably fast growing will not normally stop growing when you want it to. Do you need it to be evergreen? Do you what it all the same or a selection of different shrubs for interest?