I always check my youngest chickens first, then work my way up to the oldest ones.
One reason is that baby chicks are more fragile than older birds, so they need to be watched and cared for without fail. As the chickens get older, they need less and less attention, since they’re sturdier and know the ropes. By checking the youngest chickens first, you ensure that they’ll be taken care of before you discover any crises or distractions with the more rugged birds. This helps make sure the youngest chickens don’t get lost in the shuffle.
Then there’s the issue of disease. If you buy only from reputable hatcheries (which I recommend), then the odds of your youngest chickens arriving on the farm with any new diseases are small. This means that it’s not a disaster if you carry material from the brooder house into the henhouse on your boots or gloves. But your older chickens have had the chance to be exposed to various diseases and parasites from wild birds, to the reverse isn’t true. Baby chicks start out with a weak immune system, which gets stronger day by day, so keeping them separated from the older birds really helps. For a while, anyway.
So remember: always take care of your youngest chickens first, and then move on up in reverse order of age.