Typically PATH is set to an initial value in a highly system-dependent way by the program that logs you in (pam_env is a common contributor), then /etc/profile and ~/.profile and files that they include go on to modify that value.
Remove any change to PATH in .bashrc, environment settings don't below there: see Difference between .bashrc and .bash_profile.
First try logging in in text mode (e.g. with ssh localhost), as the session startup is a lot simpler than in graphics mode.
Put set -x at the beginning of /etc/profile and ~/.profile. The shell will print a trace of what it does on its standard error stream; look for assignments to PATH in the trace.
There is no notion of precedence to environment variable assignments: whoever assigns last wins.