The problem with using a linear regulator (zener or 78 series) with a battery, is the regulator will waste power getting to your required voltage. Using batteries that match the rating of your parts is the best option. Be aware that battery chemistry determines that actual "new" battery terminal voltage, and it can be considerably higher than the nominal rated voltage. Be sure to keep "new" batteries within the "absolute maximum" range for your parts.
Also, if using re-chargeable batteries, the charging terminal voltage can (should) get higher than the nominal cell voltages. For example, a 3.7V Lithium may charge up to 4.2V. Or a 6V lead acid might charge at 7.2V. This has to be considered. But re-chargeables make using a linear regulator more tolerable as the batteries need to be recharged but not replaced as often. Again, be sure your regulator parts can withstand the charging voltage.
-fab