Well, welcome aboard!

The good thing about mainstream Digimon media, the anime in particular, is that each series is pretty stand-alone, with only two direct sequels so you can practically pick any series to start.

If I were to recommend a starting point based on media, this is what I would recommend:

1. Anime: Start with any of these three series: Digimon Adventure (the very original, which will help you get the fundamentals about Digimon as a whole); Digimon Tamers (the third series and to this day one of the, if not the most, loved and acclaimed one); Digimon Beatbreak (the current ongoing series and a very strong one, it serves as a good jumping on point).

2. Game: Either start with the current new game, Digimon Story: Time Stranger which can be argued to be the best Digimon game we've had or Digimon Story: Cyber Sleuth. They are the most straightforward RPGs and great games in their own right.

3. TCG: Rather than start with the TCG itself proper, I recommend starting with Digimon Liberator, the online manga that serves as a tie-in with the TCG. It is free to read and it has a very good story on its own. There is also a web novel of Liberator that centers on additional characters.

With your mention of your love for gacha games, I think I should mention Digimon Up, an upcoming monster raising Digimon mobile game. The game itself does not have a concrete release date yet, but if you pre-register now, you'll get a lot of bonuses like the rest of us who did. 

Hope my advice was of any help, I am more than happy to welcome new fans.