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It sounds like you want to develop an application that won't use airtime, at least part of the time. That rules out WAP.
Most GSM and some (in the U.S. only a very few) CDMA phones can load Java applications.
Most CDMA phones can load Brew applications, which typically have to be approved by and sold through the carrier, and are typically written in C++ (though there's no specific language requirement - they are compiled to machine code.)
"Smart", or PDA phones can load applications written typically in most any language (as with Brew) and using the APIs of their respecitive operating system. (e.g. Windows Mobile, PalmOS, or - emerging - flavors of Linux).