Authorship;first,second,co
Simply, you should be the first author. 

A corresponding author will be responsible for replying to the queries come from the research community and help them to a better understanding as well as gain more citations. There are other things can you find them in the link below.

Finally, If the other author can do this task, make him the corresponding author and you can help him when needs.

This post talk about The difference between Corresponding author and First author.