Linked a bunch of potting-up discussions you might want to read through for more details.

When? Whenever you are comfortable handling them. There is no set time and you do not have to wait for true leaves they are just a bit easier to work with them. Handle only by the leaves, not the stem. If multiple plants together they need to be separated before the roots get all entangled. Do not leave more than 1 pant in a container.

If going to 16 oz solo cups then don't fill the cup. Too much soil for a young seedling. Instead fill it 1/2 full and transplant. Then as the plant grows you can add more soil around the stems. If using 9 oz cups go 3/4 full. If the plants are very leggy you can transplant deeply to just below the bottom set of leaves and bury all exposed stem. If they are not leggy then just plant them at the same depth they were.

Transplanting FAQ

No need to remove the soil. Some will fall off anyway, if not don't worry about it. Water before transplanting.

Dave

Here is a link that might be useful: potting up discusssions