Built my daughter's shed last week and it now needs a good cost of wood treatment. She's adimant that she wants it be to be green. The usual stuff I use for guinea pig hutches etc is for rough wood whereas the shed is smooth wood. I'd use creocote personally but that only comes in two shades of brown that I'm aware of.
If you want to preserve wood texture - there are green wood stains, either oil or water based, just make sure it offers UV protection. Otherwise - antiseptic (or whatever its called in uk - one against mold and insects) + latex paint.
Either old skool creosote, not the usual modern chemical free crap that's sold to the public, or old motor oil. Function over form.
Says it's for rough sawn wood the shed is smooth wood so may not penetrate. I have some here, I use to paint our chicken coup when the dreaded red mite strike. You need to be a farmer or have a small holdings licence to use it. My neighbour got reported recently to environment agency for doing his stable fences with it but he has a licence so was ok. My daughter lives in the city so I don't think.it would go down too well as it reeks, plus she wants something green in colour.
I used Cuprinol Shades on my shed. Keeps the wood dry even when the shed is being battered by a storm and is available in many colours https://www.cuprinol.co.uk/products/garden_shades.jsp. However, the claim that it protects for 6 years should, in my view, be qualified by "up to". I painted the shed, when it was new, in July 2018 and I think it wants redoing this year. I suspect that most, if not all, claims for durability on modern wood preservatives and paints, should be qualified similarly.
I too have used Cuprinol Shades and can't complain. It's adhered great and water beads off, however after a couple of years it does need a fresh coating. I doubt the paint is the issue in all honesty, it's more the wood has split and weathered allowing water ingress. The paint itself has adhered great and I certainly plan on using it again.
On my shed it looks like pine resin coming through to the surface in some places, otherwise it appears sound.
Protim is a great one for preserving timber. Can get it in various shades as well. Very thin, so easy as sin to apply. Couple of coats go on in no time at all. Not too expensive either, as you'll need to apply it every few years.