Well, one thing to note is that you are planning to use this live and presumably in settings with an audience of less than 1000.
Most answers here focus on getting the best kind of Hammond sound (or actually any) for recordings or a P.A. The least-effort answer for that is to get a keyboard/expander with a good Hammond sound.
But there is another consideration I have not seen mentioned here yet, and that is that an essential part of what is perceived as "the Hammond sound" is a rotating Leslie speaker. "The Hammond sound" on its own is supposed to be a "portable" electromechanic substitute for a church organ. And it looks like one, too, so the Hammond organ players in rock bands tend to look quite out of style with their living-room furniture-style organ.
With regard to the sound, the rotating Leslie speaker makes most of the difference, and here is the main thing: you cannot accurately record and replay a Leslie. Nothing sounds like a live Leslie speaker in reasonable vicinity. You can perfectly replicate a recording of a Leslie speaker. And the sound of a Leslie speaker from far away is also static enough (namely not interacting with the listeners' head movements in complex ways) that you don't lose much by putting it through a recording, mixer, and/or PA.
But for a smallish live audience, the Leslie cabinet will be what you want in order to be in style. The Hammond organ driving it can be reasonably replaced with electronic or digital substitutes without affecting the listeners much (of course, as a player having the full console or not is making things feel different).
Now that's still bulkish and heavy vintage equipment we are talking about, but considerably less so than a genuine Hammond organ itself.