I do not know when I will get a Playstation 4; the end of this year is looking somewhat likely.

I plan on getting Bloodborne and Kingdom Hearts III (I know that Kingdom Hearts does not have a release date, however, when it does come out I am definitely getting it).

Are there other PS4 games that you recommend I should get?

My favourite genres are: Action/Adventure, RPGs and Platformers. I also like a good horror game here and there.

I do like shooting games - just not the military shooters.

Any suggestions?

Bloodborne!

Infamous second son and upcoming witcher 3. As you are getting bloodborne be warned. It's scarier than most of the so called horror games in the market.

Get the Metro remastered edition.

Bloodborne and especially Kingdom Hearts III are awesome choices! And I see that you never had a PS3, so remasters are on the table.

You should also remember these, based on your indicated tastes:
Final Fantasy XV
Final Fantasy Type-0 HD
Final Fantasy XIV (if you'll play an MMO)
Persona 5
Uncharted 4
Dragon Quest Heroes
Final Fantasy X/X-2 HD
Transistor
Journey
Tearaway Unfolded
The Order: 1886
inFamous: Second Son and First Light
Metal Gear Solid V
The Last of Us Remastered
LittleBigPlanet 3
God of War III Remastered
Until Dawn
Deus Ex: Mankind Divided

I'm sure I am forgetting some things, but it is a start!

i know Bloodborne is an Action RPG but it does have some horror in it, actually it can be quite disturbing some times... (and i love that!), i would define the setting of the game as "Victorian Horror" which is very interesting to me since Demons Souls (the game Bloodborne is based on) has a "Medieval Horror" theme which is actually very different from the "Dark Fantasy" theme of Dark Souls.

also get the Witcher 3 it looks epic and there is a bunch of JRPGs coming to the PS4 as well but i dont know if you like those or not.

He said that he wants Kingdom Hearts III, so JRPGs are definitely on the table. :P

Although, he didn't specify whether or not he only likes action ones, or if he also likes turn-based ones. Or SRPGs, for that matter.

This. The Metro games are fun and immersive. Also 1080p60

PS4 has so much to offer. You're gonna have a blast when you pick one up.

Pretty much the best list so far on current and future titles based upon the OP's preferences.