Grated apples and carrots are both some of the first foods my kids ate. Really ripe pears are another good one...when they are super ripe, you can literally scoop it out with a spoon.
Not to be argumentative, but just because one knows what to do for a choking victim, it doesn't mean that it is always successful in saving a life. If a baby has 4 front teeth, they can bite off a piece of carrot or apple. Aside from choking on it and having an airway blocked, they can also aspirate a piece into their lung. If that happens, it needs to be removed or there is a risk of pneumonia. I have been CPR (infant/child/adult)/First Aid Certified for 20 years (in child care licensed by the state of CA), and we have always been told that prevention is the first line of defense. I wouldn't let my child have anything that could be a choking hazard just because I knew what to do if he choked. That would sort of be like letting them play too close to the pool, because if they started to drown, I could just do CPR.
I am hardly a worry-wart type of mom, nor am I over-protective. I have 9 kids, and we have had our share of stitches, broken bones and surgeries. I do watch out for obvious hazards though.