Never even considered carbureted!
Yea, fuel injection was my top priority when I bought my first motorcycle. I'm only back to carbureted with my scooter because I got a wicked deal on this.
The CB300F is nice, I just wish it had the four way blinkers the CB500F has. Also with the naked style, your body tends to act like a good wind sail. I found the 300 has just adequate power to overcome that wind resistance. You probably won't notice it as a beginner but may start to if and when you begin to outgrow a 300. Not an issue with the CBR300R with the windshield that directs air around your body. I haven't tried the naked CB500F to see if it's less noticeable with the bigger motor, but the even bigger Suzuki SV650 was not a problem.
I'd still consider a CB300F, with an aftermarket windscreen, to stay in the cheaper to insure under 400cc class. It's not as fun to ride as a Yamaha R3 (better handling, better power, better shifter) but it's a good all round bike with a nicer upright seating position and standard ABS brakes (not available on the R3).