It is a little confusing and I agree that they don't always work the way I expect. I will say that going for a single type will ultimately hold you back if you just aren't getting the proper spells. Best to just generate something that works to some degree.
Cast delay and recharge rate are the two most important stats outside of "shuffle" in which you always want "no". Cast delay is the time between spells and after all of them are cast, recharge rate is the time before casting the new full spell list.
The order in which you place spells is important and I still have to mess around with them a bit since I don't understand it as well as I thought I did. But there are casting "blocks" which is like a set of commands. This is why you want shuffle "no" because then it will always cast left to right. Casting a trispell will cast whatever spells are in the next 3 slots (at the same time) including another trispell, which will then add the next three blocks (as an example). Then you have to do some math to see what all the cast delay and recharge rate total numbers are. That's how you see what your wand will ultimately do. If you can get cast delay to 0 or lower it will chaingun but pause almost like a shotgun if the recharge rate is higher than the cast delay. The wand will always be held back by the larger of the two (cast delay or recharge rate).
IDK if this clarified or helped at all but if you have more questions I might be able to answer or provide resources for you.