I think you're on the right track with that. I like either of the text-and-tags editors better than WYSIWYG, myself, because they seem to give me better control.

The only differences between "Basic Editor - A Simple Text Box" and "Standard Editor -- Extra formatting controls" are that you get a bigger text box (about 12 lines instead of 5) and a bigger assortment of formatting controls. What you see in the text box is exactly the same in either mode: the text you've typed in, along with whatever BB Code tags you've added to it. You can upgrade from the little box to the big one on the fly with "Go Advanced" and check the results of all your tags by clicking "Preview Post".

Oh, and the button (in the top right corner of each kind of editor) lets you toggle in and out of WYSIWYG mode. Even the "Simple Text Box" offers that.

Please do let us know if changing to one of the other editor modes clears up the stray-HTML problem for you.