We (wife and I) are also just getting into keeping bees but I have worked on the fringes of beekeeping for some years in the context of parasitic mite control.
The critical thing about beehive construction is the 'beespace', the space between the frames of comb. If it's too wide, the bees fill it with disorderly 'burr comb', if it's too narrow (less than about 6 mm), they gum it up solid with 'propolis', a sticky, resiny-waxy sealing material.
Because of this, it's generally suggested for we hobbyist types that we buy ready-made or kit frames of the correct critical dimensions. (This also makes easier the buying and inserting of sheets of 'foundation' , a beeswax or plastic (or combination) material used for providing the bees a template on which to build a single layer of 'comb', the cells used for rearing young bees (brood comb) or for storing honey (honeycomb).
Once you have the frames, eight to ten of which, side-by-side, make up the contents of a brood chamber (the base 'box') or supers (anything stacked on top of the base), the rest of the structure could, with care, be made by a competent d-i-yer. (Frames also differ in height, so you may choose 'deep', 'medium' or 'shallow' boxes, depending on preference, experience in your area and the strength of your back!)
This structure has evolved from the original hive invented by L. L. Langstroth and is now a widely used standard form, in having removable frames, a major step forward in rearing and manipulating bees and harvesting honey and beeswax. Even if a single standard is not current in the UK for the whole hive (I don't know), standard frames almost certainly are and, as described, they provide the basis for the construction of the rest of the hive.
For protecting hive bodies made of deal or other soft woods, the Canadian recommendations are for a latex or alkyd undercoat plus at least two latex topcoats. Only the EXTERIOR surfaces should be painted: i.e. do not paint the inside(s) of the box(es), lid or frames! White is the traditional colour but, in any case, avoid dark colours as they may contribute to the hive's overheating in summer (bees create a considerable amount of heat on their own, without the help of the sun). Alternatively, you can use an exterior grade polyurethane stain.
My apologies for this being so long-winded (must be a newcomer's enthusiasm!) but I hope it's of help.