Honestly, there is nothing that's choke-proof. Some foods are riskier than others, but all they have to do is inhale at the wrong time and they'll gag. You're better off with foods that are cheerio sized, simply because even if your LO does inhale a piece or swallow it whole, it's small enough that air will still pass through and it won't get lodged in the throat or windpipe as easily. That's why I never liked putting large hunks of food out. Like you said, they (and you) have no control over how big of a piece breaks off. When Tyler started finger foods, we started with mushy cheerios and as he got better we progressed to non-mushy cheerios, toast bits, and cracker bits. Once he was pretty proficient there we moved on to the non-dissolvables, like soft fruits and veggies.
Personally, I was a stickler on the 3 day rule until Tyler turned 1. There were lots of foods that he hadn't tried by then, but oh well, he's got the rest of his life. After he turned 1 and his digestive system was a bit more mature, I relaxed a bit more. Well, a lot more. I only did the 3 day rule for new foods that were common allergens. Everyone does it a bit different, so it comes down to what works best for you and your LOs!