Both would work but overlap isn't very good quality and will need replacing quicker than shipap/T+G. This would work much better
http://www.gardenbuildingsdirect.co.uk/Wooden-Sheds/The-4000-Range/22566 .
I got a new shed last year for my lot and I used a local shed company. They were very competitively priced, good quality and they came and built it here all in the price plus I could have added extras such as a stable door etc. If you order online you would need to put it up yourselves.