The manufacturers are slowly moving to EFI as a standard as cars did years ago. Newer models are more likely to have EFI, but there were some pioneers out there.
The price range you have listed would limit what you can find quite a bit. Personally, I wouldn't get too hung up on what type of fuel intake the bike has and just find the best motorcycle you can get on your budget. Carbs have been around for quite a while and work pretty well most of the time.
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