I just completed first mission on PS4 and i didn't need playstation plus. Can anyone explain it why? Now i will need PS+ to play with other people online? While single player can be played without PS+?

You only need PS+ for actual multi player modes in Destiny. Even though the game is always online you can play all of the single player content without PS+ even though other people will still be in your world and you can play co op with them.

Very smart move by Sony / Bungie.

So for Co op and multiplayer one need PS+? Anyway after first mission i am now in city, and what i am supposed to do there? I think now i will need ps+ right? 

Also, I'm heading off to bed now, but I've got two more PS4 EU (I'm from UK) beta keys spare... the first two people to quote this message can have them when I pop on tomorrow...

I am playing as Titan. Same as ever, I always use tough but slower classes, because I personally am not a "twitch" player, I lack practice and experience in FPS games, so my reflexes are not that good. It helps to be stronger defensively.

I played through three Earth levels, love it so far, and the only time I died us when I ran into some character (can't remember the name) with a yellow health bar and two question marks instead of the level. I was level 3, couldn't put a dent in him, and he killed me in two shots. He was off the beaten path, though, so I avoided him 2nd time.