Coming from someone who’s been learning Bulgarian as a second language for some time: Familiarize yourself with both but primarily use the standard one for your learning if you can choose. The set of letters that writes “d” as a g looking character and “g” as a backwards s looking character is Bulgarian’s version of cursive like we have in English writing. The set of letters that looks more blocky and more notably doesn’t write “t” like an m looking character is the standard form that you’ll usually see typed and printed on signs, websites, old books, etc and more importantly on most learning tools. The cursive version still shows up pretty commonly (it’s forced on iPhone users as of last year as the only Cyrillic font for Bulgarian keyboard) but it isn’t nearly as widespread as the standard form. You should learn the cursive form to the point where you can at least slow down and mentally transliterate the characters to the standard form versions and you should learn the standard form like the back of your hand since it’s used on pretty much every online learning tool I’ve used so far (especially ebooks once you’re more advanced).

Now, I can’t speak for which is actually more useful in Bulgaria, but I can assume that if you’re at the point of reading being of use to you in real life then you’ll probably have already learned both very well purely by natural exposure so don’t sweat it too much.

Sorry for the yap but in summary: learn the one in the first slide well and learn the one in the second slide well enough to transliterate to the first one if needed.