There really is no standard. Most programs go to /usr/local or /usr/opt. Most source code goes to /usr/src. Some programs request or suggest other defaults. You should read individual program README or INSTALL files for their recommendations. Once a program is installed the .tar file is no longer needed so if you wish those can be removed unless you plan on reinstalling again later. This site is a great resource for information such as this
It has online and downloadable manuals on everything from user guides to system administration. Here is where you can find what is usually stored in which directorty.
open the "introduction to linux guide" and go to chapter 22.214.171.124
I hope this is of assistance.