MIDI Controller vs Keyboard, <$750??

Given your budget, your best bet would probably be the keyboard. Something like a Roland Juno or a Korg X50 would meet your requirements and give you a good mix of sounds. If later you wanted to expand your sounds with a module, you could control it with the keyboard. You could even set up a rack box with a line mixer & multiple sound modules, but keep in mind having all those sounds available can be great, but keeping track of everything (midi cables, levels, channels, ect.) in a live situation can get tricky. I've tried this when playing live & have found that usually the simplest approach is the most reliable. Now I just use 2 keyboards independently.