Conclusion:

The batteries were very different.  The lithium batteries were the best for the duration of the experiment.  The lithium batteries were by far the most expensive non-rechargeable battery.  The alkaline batteries were pretty good, but not as good as the lithium batteries.  The alkaline batteries have a good value since they are pretty cheap and work well.  The heavy duty batteries were not good at all, getting alkaline batteries would be a smart alternative.

For the rechargeable batteries the nickel metal hydride batteries were pretty good and the nickel cadmium batteries were not very good.  Both batteries were about the same price although a charger ($30) would be needed.  The rechargeable nickel metal hydride worked steadily most of the time and it would be the best buy if it would be recharged more than 16 times.