What are the currently most accurate sources for lists of the values for elemental properties
You should teach your student not to use numerical values with as many significant figures as possible. Knowing how to make sense to decimals is part of the scientific culture. The distance between two cities cannot be given to the least micrometer : it has no meaning. The weight of an object has no use if it is given such as $123,45678910111213 g$. The least figures which can be given for sure is the milligram (here 6). Put on a balance, such an object will display fluctuating next figures. Already the figure $7 (0.1 mg$) will fluctuate at the least draft. To be sure of the next decimals you must put your balance in an insulated and closed room without nobody entering during the whole day, in order to avoid drafts. And even, the least dust grain falling from the air will change one or two of the following figures. So please do learn to use numbers with maybe $2, 3, 4$ or $5$ significant figures. But not with ten or twenty significant figures. It is not the way science works. So why looking for the newest published values which have one or two more significant figures ? The given weight $123.45678910111213 g$ is not better than $123.456 g$. It only gives an irrational feeling of superiority. That's all. It has no meaning for usual applications. Nobody will believe you if you say that you have calculated a weight of $123.4567891011121314 g$, or measured a temperature of $12.3456789 °C$.