I really have no idea what the WHQL thing is, But as for packages available via the package manager, the idea is that all the packages are verified to work, be safe to install (i.e. not malicious), etc.. I don't know that "peer reviewed" would be the right term, but it's close enough
-- basically, on Ubuntu, the packages are the ones that Ubuntu Developers (Canonical) have made available, for some combination of reasons.
Most distributions will have the "official" repos, containing everything the developer has released included
with the distro; and, there will often be "un-official" repos, where users, forum members, contributors, etc., will put their own package submissions of software that is not included
with the official release.
Ubuntu is one that tends to (as far as I understand) have a pretty vast assortment of packages in its official repos.
Best of luck with this login thing -- and BTW welcome to LQ!