.tar, .tar.gz, .zip or any other? It might be not so obvious.
When I used Debian based Linux distributions, mostly I installed external software in the /opt directory and there are a few reasons to do it here:
/opt stands for "optional add on software packages", so basically anything that is not part of the system/opt directory where external apps are usually stored.png or xpm) and save it in /usr/share/pixmaps/ with chmod 644.
sqlitestudio.desktop, into /usr/share/applicationg and paste the entry below:
[Desktop Entry]
Name=SqliteStudio
Comment=SQLite editor
Exec=/opt/SQLiteStudio/sqlitestudio
Icon=/usr/share/pixmaps/sqlite.png
Terminal=false
Type=Application
Encoding=UTF-8
Categories=Network;Application;
Path=