I'm starting a new Wizardry 8 game (it's been a while) and I'll be using two bishops. Each one will be focusing on two schools from the four available, alchemy, divinity, psionics, and wizardry. What I'm wondering is what is the best combination for the two? Any recommendations?
There is a tradeoff.
On one side you have efficiency and versatility, on the other reliability and ability to spam spells.
If you want the former you should aim for maximum overlap in terms of spells available to multiple schools and elemental realms used by single bishop. If you want the latter you should duplicate your multi-school spells when possible.
The former will ensure you will make the best use of spell books and picks letting you learn as many available spells as possible as soon as possible and it will ensure the most efficient use of skill points and training by focusing on select elemental realms.
The latter will stop you from being caught with your pants down when your only caster capable of casting something absolutely crucial (like Soul Shield) bites the dirt or gets indisposed and will allow you to spam particularly useful ATM spells twice (this includes stuff like having two elementals active).
The things get further complicated by overlap not being uniform across spellbooks so you might have to decide which spells do you want to duplicate and which you do not.
Priests are mostly divine magic and water, psionics are mostly mental and air, with a good helping of fire, alchemists are mostly elements, so are mages, but the mages have some crucial divine spells and both have summon elemental and knock-knock.
You should probably go
here and then to spellcasting index -> individual magic schools to see the elemental realm composition and also check for spell overlaps while you are there.
Or use the manual but it lacks the nice color-coding which really helps visualization.