In the Debian (MX & antiX) world of Linux there are number of software installation tools available. I know you were eagerly awaiting my opinion on this. The tools which I use, recommend, and believe to be essential, are:
Pax vobiscum, Mark Rabideau - ManyRoads Genealogy -or- eirenicon llc. (geeky stuff)
i3wm, bspwm, hlwm, dwm, spectrwm ~ Linux #449130
"For every complex problem there is an answer that is clear, simple, and wrong." -- H. L. Mencken
The newcomer can also install gnome-software and get a pretty-looking software store, but only programs that include "appinfo" will appear in it. That said, it can help the beginner find software that they aren't aware of.
Synaptic has always been my go-to application for software management. It hasn't seen a meaningful user-facing update in a decade and every time I use it I think of some functionality that is missing. There are many things that could be improved in Synaptic, but it would require a lot of work and maybe a few tweaks on the apt back-end.
A week ago I enabled stretch-backports in Synaptic (temporarily), but it didn't show all the LibreOffice packages from backports. It only showed backports packages (updates) for packages already installed. The MXPI backports tab showed all LibreOffice backports packages so MXPI saved me. MXPI is a really nice application, but it doesn't have the scope of Synaptic and that's probably a good thing.
It seems the big guys have moved on from Synaptic. It's no longer included by default in many distros. I can't think of an application that can replace Synaptic. MXPI maybe, but Synaptic has a few views that MXPI lacks (pinned packages, (auto-removable, residual config), history, properties with dependencies). One nice little touch with MXPI is that it behaves like a GTK application. When you press the Close button the application doesn't close until you release the button, just like GTK.
Because I'm not too fond of the command line (and for some activities like web browsing but also package management I think a GUI gives a better overview) I consider Synaptic the heart of my system. Maybe the heart is the Linux kernel or bash shell, but I don't do much with those.