one small integer is not enough, two small integers are better (lab journal initials/number and sample number, like AC7-295. something like AC7-295A, then AC7-295B and so on if needed. that's how i do it anyway) this way there's no possibility of mixup with other people's samples and samples described in old lab journals
But if they do get jumbled, sorting them back out into different experiments, batches or subjects or time periods might make you prefer some extra info accesible by eye.
If you've got a robot sorter maybe a qr code - but you'd have to be pretty large scale for that to be cheaper than a human.
Sample batch two is the correct way to do it with one exception the date mechanism. YYYY.MM.DD is the correct format that should always be used in any naming convention.
The best setup I've ever seen was: YYYY.MM.DD - LTxx example 2014.07.15 - 1804 LT was the lab tech # and xx was the sample # associated with the lab tech and date.
As someone who lived through Y2K not using 4 digits for year just makes me itchy. The rest would be fantastic for a large multi building setup like Mayo.