Set the path systemwide/Set the path for a user with Slackware
 

I am wondering about the best way to modify the systemwide path and the user path with Slackware

the default system path is in /etc/profile

(assuming you use bash) you can set user path in ~/.bash_profile or even ~/.bashrc, depending on what you want to do. check the man page for bash, under the "invocation" section for reading order.