Handhelds with colour LCDs use rechargeable cells (lithium ion, nickel cadmium, or nickel metal hydride), but less expensive handhelds operate with replaceable alkaline batteries, usually AAA size. You can probably count on several weeks of average use before having to replace AAAs. Because power is more of an issue with a colour handheld, check to see how long the rechargeable batteries are rated to last with normal use. Some rechargeable batteries have higher ratings than others, but 6 to 10 hours is average.
Many handhelds have smart functions that help out with power. For instance, some have power-management settings that allow you to program the handheld to shut off after a certain length of idle time, and many include a backup battery to protect the memory when your main batteries run out.