Either way, anime is just another entertainment medium. Not merely some genre or specialized category containing bugeyed schoolgirls getting raped by giant squid. It's an entire medium. Full of different genres and subgenres within it, just like music or film. It's unlikely that it could all suck. There's a good chance that something everyone has enjoyed at some point in their lives has actually been represented in anime. Whether it's adaptations of Dumas or Dickens, horror, stories that examine suicide, smalltown life, etc.. I mean, many of the prevailing themes you'd see in other stories would be in anime. There's quite a lot juvenile stuff that I doubt many would enjoy, but that isn't everything. Just like "Aerosmith" isn't all encompassing and representative of everything in rock music.
Anyways. Good luck. If you want specific suggestions, the best kind of anime is actually the ones with schoolgirls being raped by giant squid. Fuck a Dickens adaptation.