Thank you everyone for the suggestions.
I have a Cateye wireless bicycle computer, and I'm still deciding whether to stick to it or switch to using my smartphone. I tried Strava today to see how it worked. I immediately ran into an issue one of you mentioned - I had a hard time reading the numbers on my screen in the daylight. There, the Cateye computer is the clear winner. I'd imagine battery consumption can become an issue too if I ride a long distance.
One major reason I'm considering using my smartphone instead of a dedicated bicycle computer is that a smartphone has a lot of nice features, such as GPS map navigation, music player, and ride recording, that my simple bike computer doesn't have. Not having to wear a shirt with a big pocket to carry my phone while riding is a plus, too. (I have a small porch attached to the toptube for my keys and wallet.)
I will try the smartphone method a few more times to make the final call.
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The value of your life doesn't change based on the way you travel. - Dawn Schellenberg (SDOT)