What did the sparky tell you? It looks like he's been straight with you and advised you to build in a little extra capacity in case you need to expand. It looks like you are planning on running initially from a 13amp fused outlet but with the option to upgrade to a larger (30 amp?) feed from your consumer unit if needed later.
The 2.5 steel wire armoured cable looks fine for your 13amp set up and you should get advice on how much current this will be able to carry if needed. If it is buried, this will make a difference.
Another question I would have is how you will feed both lights and sockets within the shed as the lights will need to be protected by a smaller (6 amp) fuse. Small consumer unit in the shed or a fused spur outlet?