Which foreign workers in USA who send remittances to family are getting the best bang for their buck? There are probably a lot of ways to measure that, but I want to measure it like this: Foreign national workers grouped by country of origin, which group sends the most money per capita in remittances?

That way it's kind of like saying they have the most income per capita after living expenses.

Maybe that means the skills they brought to USA are getting the best return compared to other groups.

It doesn't say anything about how far that remitted money goes in the origin country. So bang for buck is referring to getting paid in the US, not spending it abroad.

I'm not sure where to start searching for this information. I googled around but just found ads for remittance companies.
A good start would be The Economics of Migrants' Remittances by Hillel Rapoport and Frédéric Docquier. They both work extensively on this topic. In this paper, they review the  theoretical  and  empirical  economic  literature  on  migrants' remittances.

They review six theories decomposed into two broad categories individualistic motives (altruism, exchange, inheritance, and the strategic motive) and two types of familial agreements (on insurance and investment).

In all of these six theories, except one, migrant's income is indeed a very good predictor of remittances. However, other motives matter and may differ across "foreign national workers grouped by country of origin". For instance, some societies are more altruistic than others, and assuming  that  altruism  decreases  with  time  of arrival, the size of remittances should be negatively related to this variable in the altruistic case. 

They also predict contrasting effects concerning the distance from family. For instance, in the inheritance theory, the amounts remitted are expected to be closely related to the probability of receiving inheritance in the origin country. If, as they assume there is a negative correlation between the distance from family and the probability of receiving inheritance, a Mexican worker will remit more than an Ethiopian worker, other things being equal. This could even be true if the Ethiopian worker has "the most income per capita after living expenses".

To sum up, migrant's income is a crucial variable but other variables, which may differ by country of origin, may also be of first-order importance to understand remittances.