Basically those two commands posted by TryNinja is all you need to install core.
Additionally, I learned the PPA installation method poses a security risk. So I want to avoid installing Bitcoin Core using the PPA installation method. Lastly, I have already successfully verified the tarball file keys using the SHA256SUM.asc file and it checks out correctly.
Did you check whether the hash of the tarball matches the hash in the file AND whether the hash-file is signed correctly ?
Both steps are necessary to ensure you are installing the original file.
If you have any further questions, feel free to ask.