WW-
I've used a Specialized wireless computer for about four years now and I'm very happy with it. You say you want a basic model, and mine isn't the most basic there is, but it tells me all the stuff I want to know, doesn't have a lot of extras that I don't use, and it's waterproof.
As far as a battery goes, I think all computers require some kind of battery. Mine uses the tiny flat kind that's mostly used for watches. Even if you ride a lot, you can get a lot of use out of one of those tiny batteries. And they're simple to change.
I've heard there can be problems unique to wireless computers, such as false or disappearing readings when the weather is very cold. Well, I live in north Florida, so very cold weather's not usually an issue, but you should be aware of the potential problem if you plan to go wireless.
Probably others will have suggestions about less expensive computers that work just as well and are just as durable as the Specialized, so don't just go with my suggestion right away. The more you know about your choices, the wiser a shopper you'll be.
Here's my main caution: don't let the computer control your ride. Some people get new computers and then become obsessed with increasing average speed and racking up miles, just because it's now being electronically recorded. I guess that's not so bad if you're training to race. But if you're not, you can lose some of the joy of cycling that way, so resist becoming a creature of the computer.
Just my 2 cents.
--J**
"Do I contradict myself? Very well, then, I contradict myself." --Walt Whitman