Generally, you should primarily be looking at two things when deciding on the purchase: the quality of the keyboard and the quality of the sound.
Most keyboards/synthesisers will have a half-weighted keyboard which offers a somewhat different feel to an acoustic piano. Dedicated electronic pianos will generally have a weighted keyboard and possibly a hammer-action playing mechanism, designed to replicate the playing feel of an acoustic instrument.
The number of keys is a question of compromise between range and portability. A 61-key keyboard will be easy to transport to rehearsals/gigs, but you may find it too limiting for classical piano repertoire. Many companies sell a number of versions of their keyboards/synthesisers, so you may be able to choose between 61, 76 or 88 keys. If five octaves seems too limiting and the 88-key version is too big, the 76-key option may be a good compromise. It's also worth noting that 61 and 76-key keyboards tend to be half-weighted, while 88-key keyboards are generally full-wieghted.
With regards to sound options, digital pianos tend to have a limited sound selection: generally several acoustic and electric piano models, plus maybe some strings or organ sounds. If require a more flexible sound bank, you would need to connect an external sound module or a computer running a software synth via MIDI.
Synthesisers will of course have a lot more preset sounds and editing tools for creating your own. I'd generally advise against purchasing a keyboard, unless auto-accompaniament is a required feature. For most purposes in a band setting, a synthesiser/workstation is a better option. The drawback is that most synthesisers don't have built-in speakers. However, in most performance situations this isn't a drawback and the synthesiser will have proper stereo line outputs, which isn't always the case with keyboards (having these is essential in any recording/performance situation).
For the applications you've outlined, my suggestion would be to look for a synthesiser/workstation with a 76 or 88-key keyboard. It will give you a broad selection of sounds and at the same time offer enough range to play some classical repertoire. If the classical repertoire is a key consideration, however, I strongly recommend getting an instrument with an 88-key full-weighted keyboard.