I didn't worry about choking, as DS2 is my second child (duh), and DS1 never really choked, except on really obvious stuff (big piece of meat, big piece of squid).
Apparently the risk of choking is a lot lower if they put the food in their mouths, rather than sucking it in with a bunch of puree. So far, DS2 hasn't choked at all. He's gagged a bunch, but I just watch closely to see he's still breathing, and leave him to it. (He gagged a lot on a piece of lamb at tea today, and my neighbour, who had him on her lap, was all ready to start clapping him on the back and flapping, but we left him to it, and he was fine.)
You do, of course, have to watch them while they're eating, particularly at the start, and particularly with anything easy to choke on. And you have to know what to do if they do start choking.