If it’s your phone you don’t have to use the web browser. And “The Internet” is a lot more than webpages. It’s a set of common standards for data exchange and the machines which use them. Automatic operating system updates are “Internet”. Downloading the siddur onto your phone is “Internet”. The application which tells me where the nearest shul is and alerts me when Shabbos is less than an hour away are “Internet”. The public key protocols I use at work to verify the integrity of data on remote servers are “Internet”. Unless you’re a number theory freak they are about as exciting as watching (dark gray) paint dry.
In fact, most phone calls these days are “Internet”. You can’t get away from it. Two of the best applications out there – Evernote and DropBox – store your notes and files on Internet servers. It seems like your stuff is on your phone, but it’s really out in the cloud somewhere.
If you are worried that someone might use your phone to access bad websites there’s a simple solution. Set your phone up to require a password to unlock except for answering calls. I know Android-based units and iPhones can do that. I’m sure the Blackberry can as well.
As for Palm, I’d say ditch it right away. Palm is dying. Their market share is circling the drain. Their application store is a joke. Symbian-based phones, Nokai and Windows Mobile are all crashing. I’ve seen the future. It’s dominated by Apple, Android and a slowly shrinking slice for RIM.