I have thought about this for a wile and i think i would recommend in order.
1. Attack On Titan
So why would i recommend this for someone just starting to watch anime? Well, Attack On Titan is a action filled anime with episodes that gives you a good mix of tension and suspense. For each episode i watched i felt like i was putting together a puzzle, and it felt like the series at a notable bases gave you just enough information to keep you watching. But not so much information that you couldn't make theories of what was going on.
2. Mobile Suit Gun dam: Iron-Blooded Orphans
This is one of my favorite animes so i am a bit biased here, but i truly believe that this anime is a bit underrated. I feel that this anime has a dark wibe where you are watching factions fight for their believes to become reality. Mari Okada is the writer of the series, so people usually love the style she uses or just straight out hates it. The drama and the tension she builds throughout the series is thrilling and who doesn't love a good bashing in space between robots. If you haven't seen this one, you should definitely drop what you are doing and watch season 1 and 2.
3. Saga of Tanya the Evil
I feel like this anime just takes the cake, it feels like you are watching a science experiment where everything is stacked against the subject. It's one of those animes where the main character is cold, calculated and mixed with a sprinkle of insanity.
4. Hunter X Hunter
So this anime might not be the greatest anime for people that are just starting to watch anime. But some might like it, it really depends on what kind of things you like to watch. So the reasoning i put behind this one is that it is a long anime that has great character building. The action draws you in, and the battles get more and more exciting when the characters get stronger. It has some dramatic moments, and i can't forget the moments when characters loose control #anger...
5. Code Geass
So the final anime i would recommend is Code Geass. If you like the underdog destroying the much stronger enemy then this might be something. Action packed with fighting, drama and loss, this might be one of the best animes i have seen. (of course, that is my opinion....) If you like bigger army diplomacy this might be something you will like. It will pull you in to the cold calculated mind of the main character, and push you over the edge to insanity lol. Take a look and hope you like this one.
Well as stated this is just my opinion on some starters people should watch, i love all of them. But you might not, have a good evening guys and i will be back on forums again in the future :D