Since the original poster quoted AA and Zone System tests, I'll answer with that in mind. Zone system tests go as follows:
1) First, make a film speed test.
2) Second, make a test to determine your Normal (N) development time.
3) Third, make subsequent tests to determine N+1 and N-1 times at least. Possibly do N+2 and N-2 also.
It sounds like you've already done the speed test. Your ASA setting should result in an exposure for Zone I that will read as .1 above film base plus fog (FB+F) on a densitometer. That is the definition of film speed. The developer and development time that you use will have little effect on the outcome, unless you go to some odd extremes. Just use a standard film developer for the recommended time for that film and the speed test will be accurate.
To get the Zone I exposure, you set the meter at the manufactureres rating for the film. Find a surface that is of even texture and reflectance and illuminate it evenly. I use a large piece of construction paper from an art supply store that is as close to middle gray as I can get. I illuminate it with flood lamps while pinned up on a wall. Then I take a meter reading and stop down 4 stops, 'placing' the card on Zone I. I point the camera at it and focus at infinity so the card is completely blurred and any surface texture is not in focus. Then you make an exposure. Then close down 1/3 stop, make another exposure, close down 1/3 stop more and make another exposure. Open up 2/3 stop to get back to original setting. Open up 1/3 stop more and make an exposure, then open up 1/3 stop more and make another exposure.
So, you end up with 5 exposures at the rated speed and 1/3 and 2/3 stop more and less exposure. If you feel it's necessary, you can make 7 or 9 exposures if you want to. I would do this if the film was real old or I knew my shutter speeds were off or the meter wasn't all that accurate\consistent. 5 eposures should be ok, but 7 is fine, too.
For sheet film, I have a neat trick where I can get 6 seperate exposures on a single sheet of 4x5 film. If anyone wants to know how to do that, let me know. It's VERY handy come testing time and saves a lot of film.
Develop the film with something like Rodinal at a recommended dilution and time. Don't vary greatly from the recommended time, but you don't have to stick exactly to it since you haven't done your own development time tests yet. Earlier comments about film speed varying based on development time are true, but only at greatly increased\reduced development times and it varies by film. The speed changes because at expanded development times the 'toe' of the film comes 'up' - if you plotted a characterisctic curve of a film at different development times, you can actually see the densities of the Zone I values increase as development time increases, but they don't increase a whole lot.
The slope of the curve changes, too, thus the reference to contrast changing at different development times. This slope indicates the contrast index of the film. You really want to use a film that will increase this slope at increased development times and lower the slope at reduced development times. This is what gives you the expansion\contraction contrast control that is so important to the Zone System. As I understand it, a film like Berger BPF doesn't do this well, but a film like EFKE 100 (or Tri-X among others) will do it well.
The whole point I want to make is that for the the speed test, don't worry about the development time too much, just stick to a normal time\temp.
You asked if, after determining your personal ASA speed, what development times do you follow. Well, you have to test that yourself! That's the second major test of the Zone System. You don't follow standard charts anymore - you've stepped into the relm of customization and a level of accuracy where charts are useless. Charts? We don't need no stinkin' charts!
My method of determining development time is to first determine what density range my paper is capable of handling (probably about 1.13 for food fiber paper). I determine this by contacting a calibrated density step wedge onto the paper and just counting the number of wedges that go from pure black to pure white and sutbract the 2 densities from each other. I will probably end up around 1.13 or so, but I hear it is more like 1.35 for Azo (which can handle a very large density range but is for contact printing only).
If you add .1 onto 1.13, I get 1.45 so I know that the greatest density that any of my negatives should have, to be printable, would be 1.23 which would print as pure paper base white in the print. One stop lower than that is textureless white (Zone IX) and one stop less than that is white that starts to show texture (like the threads in cloth) at Zone VIII.
So, the point of the film speed test is to determine a film development time that will take a Zone X exposure and will produce a density of 1.23 in the negative. Simple enough. Set up card\camera again as before. Meter card, upen up 5 stops and make a series of exposures. If you're using roll film, expose the whole roll. All exposures are at Zone X.
Cut the roll up into 3 pieces and devvelop one piece at the recommended time\temp for this film\developer. Measure densities. If the density is greater than 1.23, develop the next strip for about 10% less time and measure again. Keep changing development times until you get a time that will produce a density of 1.23 in the Zone X exposures. It does not have to be EXACTLY 1.23 but should be close. If I got 1.19 I'd call that good enough.
As soon as you have a development time that will produce a density that will print as a Zone X tone in the paper, then you've got your standard development time.
As a check on the accuracy of this density, you can do 2 things.
1) Photograph some Zone VIII subjects, subjects that should print as white but with texture, like fabric, snow, feathers, etc.
2) Take a film speed test strip and print it on your paper of choice. You can enlarge the negatives to 8x10 and put the film strip in the carrier so that a clear edge is projected onto some paper. Do a test strip and determine the SHORTEST amount of time necessary to print the film strip edges (unexposed but fully developed) as pure balck. Set the enlarger at a height that you can write down and make note of the lens aperture. Write them down.
Then, develop the Zone III subjects for your 'normal' time. Put a negative in the enlarger at the same 8x10 height and lens aperture and make a single exposure at the time it took to produce maximum black thru film edge. Don't do a test stipr now, just pop in the negative and expose for this time. If all your calibration is correct, the Zone III densities should print as a Zone III or very close to it. This will be the acid test of your calibration process above. If this comes out right, you now have your own ASA speed and development time that will produce negatives of a know density range that is calibrated to your paper. As you try different papers, you should print the step wedge again to determine the density range the paper is capable of. If suddenly some brand is only good for a range of 1.00, then your 'normal' negatives will be too contrasty for this paper. If you contact printed your 'normal' negatives on Azo, you'd suddenly find the prints being way too soft. In these cases, you'd have to re-calibrate your negative densities to the paper again.
After you determine your 'normal' development time, you next have to after N+1 and N-1 negative development times. Basically, N+1 is defined as the time it takes to take a Zone III exposure and end up with a Zone IX density. N-1 is the time it takes to take a Zone IX exposure and end up with a Zone VIII density in the negative. If you need some explanation of this process, let me know.
AFter I had done all these tests in the past, I knew that I could take a piece of Grade 2 Zone VI Brilliant paper and enlarge one of my negatives for 12 seconds and I'd always get a full-tone print, or at least a print that accurately reproduced the densitives in the negatives that I had created. That is because it took 12 seconds to create a maximum black thru the FB+F with my film with the enlarger at a certain height and the lens at a certain aperture. All tones above Zone I printed in relation to their densities above FB+F. So, if my negative had a Zone VIII density, it printed as a Zone III tone in the print with this 12 second exposure.
Over time the Zone System has been refined and some of it's underpinnings have been argued over by those who are really technical and inclined to test a lot. But the above process works quite well, will give you a personal ASA speed and a set of negative development times that will create negatives tailored to the characteristics of your paper.
Good luck.
-Mike