So, in case you were ever curious what it would look like, here's what it would look like if you took the matrix of what types are supereffective against what other types and interpreted it as an adjacency matrix. Honestly, this is kinda cool, if not the most useful thing out there.
This graph brought to you by the question of if Nintendo could do anything other than fire/grass/water starters. Answer: Yes. There is at least one other cycle in that graph: fighting beats dark beats psychic beats fighting. There are probably others, but I'd have to spend more time looking at it.
Or, I guess I could probably use code to do it for me. But that's a thing for later.
Of all the possibilities, I think I'd most be interested in fighting/steel/fairy, or maybe ice/flying/fighting. But any of them would be an interesting departure from the standard fire/grass/water we normally get.
Also, yeah. When it came to writing the code for this, the hardest part was coding in the adjacency matrix for the graph. Otherwise, it was so easy that the code actually compiled worked right the first time! How often does that happen?! If I wanted to improve the duplicate avoidance, it'd probably be pretty tricky, but why bother? The code did what I needed it to!
Okay, well, it turns out, the code was actually pretty trivial. So, here you go, a list of alternatives to the fire/grass/water starter trio!
(I didn't do the greatest job in coding to avoid duplicates, but I'll remove any that popped up from the alt-text)