In all honesty, I hate positioning with such a passion that for awhile now I’ve been a floated layouts only kinda guy mostly because it causes less stress for me across different platforms. Now this may be wise, but it’s also like trying to run a marathon with one leg.
Positioning is important but what does it exactly do? Found a nice article that put it very simple and basic like for me.
Position-Static: Normal, nothing is changed. This is the default, but you can set it specifically to this to make it normal again.
Position-Relative: Relative to normal. So you place an element in the flow, then tell it to go 40px left with position relative and it’ll move 40px left relative to where it was normally placed.
Position-Absolute: This takes the element out of normal flow and places it wherever you want. All the other elements will sort of ignore the element you’ve placed absolutely.
Position-Fixed: Also takes it out of the flow but displays the element relative to the browser position. (Doesn’t work in Internet Explorer)
So with this newfound knowledge I’m going to go for some more experimentation I’ve been meaning to do with overlapping navigation I’ve seen on some websites that might look cool.
Also found some nice stuff here and some info about positioning in CSS3 here.
CSS Schema 
Hey,
I also prefer the floated layouts over the others. It is easier for me, and I have no problems getting the look that I am looking for (so far). The other positions tend to through me off, especially if I design a site geared around Firefox and see that it is totally jacked-up in IE.
I agree; positioning in web design can be pretty frustrating. I also like your analogy of restricting yourself to one positioning style is kind of like running a marathon with one leg. I like that you broke down the types of positioning in CSS very clearly- it seems like you have a good handle on what the different strategies are.