At the very least, you need the Atmosphere, hekate, sys-patch and a title installer like DBI, Goldleaf, sphaira, etc. I'm currently on firmware 21.1.0, Atmosphere 1.10.1, hekate 6.4.2 and sys-patch 1.5.9 and I use latest Russian version of the DBI in order to install my games. While DBI's developer isn't the most beloved developer around here, I do believe that DBI is one of the best if not the best title installer (among many other things) for the Switch. English alternatives are sphaira, Goldleaf, Tinwoo, Awoo, Tinfoil, etc. and while some of them work most of the time, you might run into an issue here and there. Check
this video to see how to use DBI. I'm yet to run into an issue with it. I'd suggest against using the latest unofficial English patch for the DBI as the original uploader apparently added some sort of a check that if the unofficial version is detected or the app has been tempered with, the app will start breaking gradually (games not installing, features not running, etc.). Whether that is true or not, I'm yet to see the confirmation from someone else other than the author. Russian version works just fine and, unless you intend to be a power user, it's not hard to learn which option does what. Alternatively, I'd suggest checking out sphaira as it's probably the next best thing, followed by Tinwoo/Awoo Installer, whichever is newer.
You don't need both sigpatches and sys-patch, having sys-patch is more than enough and I personally recommend using it. Atmosphere won't work out of the box with the sigpatches, however it will work with sys-patch. After you install sys-patch, you need to reboot your console at least once so that patches get applied on boot (after which sys-patch turns off and is not needed anymore). I'd suggest getting
Ultrahand as well so that you can check whether sys-patch is working properly. Alternatively, you should have a log file somewhere in the config/sys-patch folder, if I remember correctly.
If you ever need to update your Switch, check
this thread.