While i agree in principal about the level of distraction using a phone in the car, the argument about taking your hands off the wheel is not really relevant, unless your car has auto lights, wipers and gearbox etc.
Its the fact that your mind isn’t on the driving that’s the problem, i do 130k miles a year ( coach driver) and its quite easy to spot a driver who is distracted (whether its a phone call, talking to passenger, fumbling in handbag or whatever)
Btw, im certainly not claiming to be any kind of driving god, but i do pay attention to the road and surrounding environment, thats the main thing imo.
Anyway, back to the OP, i may be a little late (typical bus driver etc) , but my wife had a Bluetooth head unit in her previous car, a sony one, it was around £70, worked well, if i was buying another id say go for one with a separate mic, they sound better at the other end of the call.