Ok, I think I understand already how the solver works (sort of, after a lot of reading and thinking).
But, maybe I am using wrong terminology. I mean the default pole vector that comes with the IK. I have not tried to constrain it yet, but I have been wonding how it decides to put it where it puts it and how to change that. My rigging needs are sort of simple and I am using the IK more as handles than real IK.
So, I will have on the upper arm for example, one shoulder joint, a bicep joint that only rotates in x that's just for making skinning easier on me since I am a novice, and then elbow. Then I make chain from shoulder to elbow and I get a pole vector automatically that points backwards. But what I really want in my special case is for it to point into the body towards the hip. Since it's not real IK I theoretically should not have to really move it around ever because I am only doing one joint on it anyway.
So is my only way to change this using a constraint? If so, I will read up more but I was hoping to avoid this because it seems to be very confusing in its setup. Probably easy once you have done it and know how, but it seems I spend a huge amount of time figuring out some of this seemingly trivial stuff.
Also, is the 'set preferred angle' something to do with this? Since my joints are all in an exact line I don't know how setting the preferred angle would affect this. That is, the shoulder, bicep, and elbow.
Thanks for your help so far. Maybe I am more clear now.
Oh, and maybe I should go into what I am trying to achieve in general. Maybe it's just misguided. I don't really need real IK, I guess. I am just doing game animations and they are not very long or complex so I'd mostly rather use FK. But, I find actually rotating the joints to be super tedious. So, I am using the IK chains of basically two joints (sometimes with nonmobile ones between. That way I can just drag around controls instead of doing rotationg. Plus, I plan to do some aim constraints as well. I guess an odd rig, but that seems to be the style that feels natural to me. I have played with real IK rigs but they seem a bit unnatural and I seem to also get odd results as well. Probably for spine I will do something more standard, though.
I was also thinking I might use spline IK and that would be simpler. Like a spline IK that has just two points for each joint. I am not sure how it works, though, and I am planning to do this for a game engine so I am not too clear on whether spline IK is going to come through the export process unmolested so if possible I'd like to use this (admittedly goofy) method as well. I am happy with it so far, except this one issue needs to be resolved.