What I haven't seen mentioned here is the fact that the toe and shoulder areas of the print (the highlights and the shadow areas, respectively) have inherently less contrast than the mid-tones. Increasing exposure somewhat moves the part of the print that was previously in the toe more toward the mid-tones, thereby increasing the separation (read contrast) in that area. The converse is true for shadows: giving less exposure will move them toward the middle, thereby increasing contrast. And, the opposite is true, one can reduce shadow and highlight contrast by increasing and reducing exposure, respectively. So, especially in these critical areas of the print, exposure changes effect contrast changes. Balancing a print this way, in addition to the basic choices we make for overall contrast, coupled with effective dodging and burning is what it's all about.
To possibly help the OP and others here who have expressed frustration at getting "lost" somewhere between exposure and contrast adjustments: First, we all have been there (and still fall into the cracks occasionally!). Maybe my experience and method will help others streamline their printing.
I find that staying with one contrast for a while and dealing with exposure changes first helps me a lot. I, like Bill, use graded papers primarily, but the same strategy works fine with VC papers as well. I determine my starting contrast from my contact proofs. (Actually, I indicate intended paper grade on my exposure record at the time of exposure, and it works out in most cases). Then, I make a test strip, concentrating on the highlights and the separation and tonalities I want there in order to determine starting exposure. I then make a straight print at that exposure and evaluate it for overall contrast and exposure. Unless the contrast is way out the window, I adjust the exposure by small increments to arrive at the best print. I incorporate dodging and burning at this point, seeing what does what in that department as well. I'll tweak development time and dilution (maybe add some restrainer or carbonate) also, all to try to get an optimum print from the chosen contrast grade.
Only after it is really apparent that the chosen contrast grade will not work do I decide to change contrast. For me, this is by switching to a different paper grade, choosing a different paper with inherently different characteristics, or changing development schemes (softer developer, etc.), but it really is just a "change in contrast" however one wants to achieve it. When I use VC papers, I do essentially the same thing, changing contrast only after I've really determined that my starting contrast won't work.
I then start over from the the top: make a new test-strip and determine a new starting exposure for the new contrast print. This may seem to be more work than necessary, but I find that in the long run it saves time and materials. Remember, the critical highlights will NOT be the same with a new contrast, either in exposure or in rendering, and you really need to find the exposure for these before dealing with everything else. I then refine exposure, dodging and burning, etc. as before. Sometimes it takes three of these "start-overs" to find the right contrast for a print, but usually it is only one or two.
After that, it boils down to refining the print manipulations and making purely subjective, and more artistic decisions. Sometimes, I'll like a print at more than one contrast/exposure... but that's another discussion.
In a nutshell, I think it's better to stick with one contrast first (as long as it is in the ballpark), make your best print and then refine contrast as desired, not seesaw between changes in exposure and contrast: maximizing two variables at the same time is just too time-consuming.
Hope this helps,