What is anime?
Anime are cartoons or animations produced in Japan. While some American shows look like "anime," they can't be called anime unless it's been created in Japan or by a Japanese company. Otherwise, it's a cartoon/animation.
Best anime to watch?
I'd suggest starting off with something easy to swallow. There are people who argue that dubs are the worst thing to happen to anime, but it's entirely up to you. I personally think most dubs sound excellent, and prefer those over subbed anime. However, sometimes dubs are not available, or the dub sounds like trash (poor audio recording, bad lip syncing, ruined music/ambiance, etc. etc.), in that case subs are the way to go.

Here's a list of my favorite anime... I'll list the genre so you know what to expect.

One Punch Man - Action/comedy/parody. (dub/sub)
School Live - Horror/slice of life (sub)
One Piece - Action/adventure/pirates/comedy/never ending.... (870+ episodes) (dub/sub) (I personally wouldn't start with this one)
Konosuba - Isekai(transported to another world)/comedy/action (dub/sub)
Assassination Classroom - Action/Slice of life/highschool (dub/sub)
Parasyte - Fighter/"body horror"/sci-fi (dub/sub)

I'm a weeb... ¯\_(ツ)_/¯

 

Avatar: The Last Airbender was a good show to watch

In some ways it was romantic which was really nice