Slightly off-topic, but I have seen a few anime TV shows when I was a kid. Things like Dragon Ball Z and Pokémon, but I haven't seen anything modern yet.
If you like Dragon Ball Z, then try watching Dragon Ball Super.
It's a worthy sequel, a lot better than Dragon Ball GT.
Are Cowboy Bebop and Full Metal Alchemist overrated?
No, they are good for their time.
Full Metal Alchemist Brotherhood is better than the original FMA though,
since it's stayed true to the original manga version.
Does anyone have any recommendations?
My recommendation, try these two :
Demon Slayer: Kimetsu no Yaiba
Cautious Hero: The Hero Is Overpowered but Overly Cautious
Should I subscribe to Crunchyroll to watch shows like this?
Only if you're interested in Shenmue