Hi Obs! will your new shed be made from timber which has already been treated with some preservative or other? If so, "ordinary" paint on top might not work so well.
I had to have the doors to my shed/garage replaced a few years ago - needed to make the opening bigger so as to get the car in - and ever since then I've regretted not using creosote on the (new) doors. The shed itself dates back to about 1960 (nearly all of the wood is still more or-less OK) - & was used as a sort of workshop, I think, & has been creosoted a number of times over the years.
I painted the doors dark green - using one of those paints which "do what it says on the tin", and despite the fact that the wood was new & had been primed & undercoated, the green paint peeled off after a couple of years. The doors face south & get the full sun, soo that may have had something to do with the problem - though the other parts of the front (creosoted) are as good as ever.
How I wish I'd used creosote on the doors in the first place, & not green paint................