I've used Spectacle with the defaults, for years. It's not actively developed but still works. There are actively-maintained alternatives, but since it has zero times done anything weird or glitchy for me, even with multiple monitors, I've not switched yet.

"brew install spectacle", start it, give it accessibility permissions it needs in the Settings panel, set to start at login (check a checkbox in Spectacle's settings panel). Forget about it until you set up a new Mac.

cmd+option+up/down/left/right for half-screen tile. Cmd+option+F for the equivalent of maximizing a window in Windows (not Mac-style fullscreen). Cmd+ctrl+left/right for upper-left and upper-right quarter tiles. Add shift to make it lower-quarter on that side. That's it. Was all available to me instantly via muscle memory inside a month, don't even think about it now. It's how I do nearly all my window placement/resizing.