At work, we purchased a bunch of Mitutoyo solar calipers. Those are awesome, accurate and never need batteries. They are also expensive.

At home, I use a $12 digital. The battery cover broke. It reads down to 0.001", but, I wouldn't trust it to better that 0.005". For home use, 0.01" accuracy is all you need. If you need better, you're doing real machining. And when I get tired of the battery situation, I'll buy another $12.

Also, when you start getting into <0.005" technique becomes important, even the best Mitutoyo can steer you wrong if you don't know what you're doing.