A trench coat is an essential transitional piece. Personally I would never buy a trench coat that wasn't waterproof - a good trench should be able to withstand the rain that often appears out of nowhere in Spring. Ted Baker and Tommy Hilfiger are good retailers to look at for classic trenchcoats.
It's also a good idea to switch up your colour palette when you move from one season to the next. This means that you can slowly transition your outfits from Winter to Spring and then also carry on wearing some of those Spring pieces in Summer too. I like to bring out blush and dusky pinks when the weather starts to get warmer - that signals to me that Spring is on its way!