Anything can be intimidating
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Attack on Titan is Shingeki no Kyojin for example.
While I was writing this GoldenX said to watch FMA:B and as you'll see that's basically the right answer to everything.
Of what I can remember I've watched here we go;
What I do recommend #1 is Fullmetal Alchemist Brotherhood, and then just maybe Attack on Titan. AoT isn't particularly great but it's got action and a formula that isn't wildly out of place if you've watched at least one each of a horror movie and over the top action movie. Fullmetal is fantastic in nearly every way. Sure that might be coming from a little rose-tint on my end, and I'm the kind of person to like it anyway, but I think most everyone would like it. Brotherhood is newer and better than the first one though so watch that one.
Castlevania is simply animated, not anime, but it's pretty good. Might wait for season 2 to come out though, season one is very very short.
One Punch Man is tons of fun but I'm not sure it's great for a first time anime viewer. It includes a ton of jokes that poke fun at typical anime stuff, but I'm not sure you need any more than a basic knowledge of anime to get it. Fight scenes are 10/10 though.
Sadly I recommend against Knights of Sidonia for a while. I'm not sure how I got suckered into it, but I'll admit it's fairly interesting and entertaining, and giant robots are always cool. Thing is, it's very classically anime-y. Quite a bit of "main character is hopelessly awkward and so is everyone else and nearly every male-female relationship dynamic is at least 50% weirder than it needs to be" Oh and some of those dynamics are 150% weirder than that. The whole show had me thinking about how it was
really weird almost all the time, but I watched it anyway.
Cowboy Bebop is also a classic, I haven't watched it though. And apparently if you just hate yourself and emotional stability you can watch Clannad. I haven't psyched myself up enough for that one yet.