If it has an oil based finish on it now an oil based stain will work like your Australian Timber oil which isn't a bad choice for a big box store product. Just a good pressure washing and letting it get totally dry is all you should really need for prep. The suggestion of Penofin is a good choice and may hold up longer. I've not used it but General Finishes' Outdoor Oil I suspect would be good. I've had outstanding luck with some of their other products and their products are almost universally loved in the woodworking community and considered top tier.
Personally I think the oil stains look the best but there are none out there that will last. The more opaque it is the better durability you'll get. Oils are always going to be a 1 to 3 year maintenance requirement. Painting it will last longer but doesn't look as good IMO, I like to see the grain.