It really depends on what you’re looking for. Are you just looking to learn how to print new materials, or do you have specific requirements for a project?
If it’s the former, I’d say the easiest thing to try is PETG. It prints pretty reasonably on most printers though has stringing issues. It has different mechanical properties that make it suitable for other applications (for example, better temperature resistance and impact strength). It’ll be much less frustrating than trying to dial in ABS for the first time.
ABS and TPU are both a pretty large step up in difficulty, but are quite good for functional parts. If you insist on learning one of these, pick whichever one fits with your projects better. For ABS you’ll want an enclosure and a well ventilated room (IMO I wouldn’t be in the same room as the printer) as it emits harmful chemicals during printing.
IIRC BOTW was built on MonolithSoft’s engine (the devs behind Xenoblade) so in fairness, those games are more-so the same exception rather than the rule. That said, even without the comparison, GameFreak clearly did not properly optimize the Pokemon games on switch, with stuff like loading the whole map’s ocean at any given time.