First, this is the only E3 presentation you genuinely should watch.
Games-wise, here's what I decided to grab:
Hellblade: Senua's Sacrifice. Third-person adventure game, where you play as a mentally ill Celt (or Pict, I've heard both) who is going into Viking territory for a specific purpose. The puzzle mechanics are interesting but a tad dull, and the combat is pretty repetitive. But holy shit the atmosphere and storytelling are off the chain. See, the conceit is that Senua is genuinely insane - she's psychotic, and so you hear what's in her head. The developers talked to actual psychologists and people with hallucinations to make sure they got it right, and it's done incredibly well. Dark without being edgy. (I actually bought this during the GOG sale earlier in the week, so I've been able to spend some time with it.)
Slime Rancher. At the complete opposite end of the aesthetic and emotional spectrum. It's a first-person ranching game where you're on a planet, and as the name implies you farm slimes. Incredibly bright, colorful, and cute, but without being saccrine. Gameplay is deep enough to be interesting without being super complex.
Just Cause 3 XL. Pretty much a no-brainer at $6.74. If you're unfamiliar, basically this is GTA, except you are a mercenary in a foreign land and the game isn't even pretending that it's realistic. Encourages just going around creating as much mayhem as possible.
Objects in Space. If FTL was a trading-emphasized sandbox, and you have one crew member whom you play through a first-person perspective. Many of the reviews compare it to Silent Hunter in space, because combat is hard and you're generally trying to hide (by doing things like staying in nebulae and shutting down various things to make you harder to detect). It's the same price on GOG if you'd prefer to go that route. It's technically in early access or whatever, but is pretty much feature complete.
I'm also seriously debating getting Final Fantasy XV, since it's only $25 right now and I've heard really good things. I just don't know if I really have the free time to get into something that time-consuming. I've been preferring story-heavy action games (I recently marathoned both Dishonored games, which I liked quite a bit), and they tend to do better with short play sessions.