Which version of Oracle instant client download should I use for Oracle 10g?
Oracle client versions are generally backward compatible. Unless the server is too old. As long as it is a version greater then 10 it should be fine.
Have a look at the link below. There is a matrix showing interoperability details between client and server versions.
http://orcl.tistory.com/entry/Oracle-Client-Server-Interoperability-Support