Thanks for the list, unfortunately, it does not list games that were later ported to PS4.
I will try to comment on all games that have been mentioned so far (and thanks for everyone giving recommendations):
Games I have now on my list to buy - in addition to the ones in op
Valkyria Chronicles (Only physical version available, I forgot about it)
Initial D (Japanese import game)
Games on my maybe list
Uncharted 1-3 (I did not like Golden Abyss and saw it as a sub-par tps with eye candy, but I have played all PS1/PS2 Naughty Dog games and might give that series another try)
ICO & Shadow of the Colossus Collection (appear to be a bit empty and not focussed on gameplay that much, but they are not excessively expensive and fit one of my favourite genres)
Infamous 1&2 (I will need to look into them a bit more, I thought they were a bit like GTA, which I do not like, but people here have talked about its platforming aspects that seem to be good)
Heavy rain (I like visual novels so it could be a good choice)
Motorstorm: Pacific Rift & Apocalypse (probably not arcady enough for me, but we'll see; probably very cheap)
Puppeteer (a platformer, so judging by genre a good choice. It looks a bit like LBP though, in terms of physics...)
Tales of Symphonia HD (probably cheaper than getting the GameCube version)
Games I will likely skip but do not rule out altogether
Last of Us (I dislike stealth, shooter, resource management and setpiece design - so basically everything except the story, most likely)
Journey (I do not like the "artsy feely indie games" as I call them, but I did enjoy RiME a bit)
Tales of Xillia (I like RPGs but I have no Tales games, however, I have been told I should buy Symphonia first and play from there. Until I reach Xilia, I probably lose my interest in the series)
Drakengard 3 (I do not know games 1 & 2)
No no kuni (If I want it, I can get it on Switch)
Heavenly Sword (I do like their DMC, so it is possible I will like that as well, but it got a bad reputation so it is not something I am very interested in)
Games I need to get some info before because I do not know them
Folklore
Siren Blood Curse
Time crisis razing storm (does this make sense without pointer?)
Siren blood curse
Games I will certainly not buy
Resistance 3 (shooter)
Demon's Souls (soulslike)
Dragon's Crown
MGS Collection and Metal gear solid 4 (stealth)
Gran turismo 5 (sim)
Little big planet (played it several times. I think it is the worst platformer I have ever played and despise the physics)
Killzone 2 (shooter)
Sly collection + Sly 4 (already have them on Vita / PS2)
Prince of Persia HD Trilogy (fantastic games, but I already have them on GameCube)
Afrika (Sim)
Ratchet & Clank games (I already have them, except for the two spin off games)
Jak & Daxter collection (already have them on Vita / PS2)
Deadspace (shooter, also available on Xbox 360)
UFC Undisputed 3 (sports)
Soldner-X (I already have it on Vita, it's great)
ModNation racers (I already have it on Vita, it is a bit boring imo, but not bad. Just significantly worse than Mario Kart and Sonic All-Stars games)
Echochrome (I already have it for PSP, nice game)
Numblast (I need to hack the PS3 to use an Xbox controller, so no PSN games)
Yakuza (I hate Shenmue and GTA and this is basically a combination of both, right?)
Catherine (I have it for Xbox 360, it's good)
Persona 4 and 5 (I have Persona 2 for PSP and found it extremely boring, so not for me probably)
Wipeout HD (I have several Wipeout games, and the controls are just too floaty for me)
Eternal Sonata (also available for Xbox)
Katamari Forever (I have a Katamari for Vita and while it was fun, it overstayed its welcome for me. I do not need more of that)
Tokyo Jungle (Survival)
Super Stardust HD (PSN, not possible with a hacked PS3, which is necessary for my contoller of choice; would be a great fit otherwise)
PlayStation All-Stars Battle Royale (I have it on Vita and it is quite nice)
Lolipop Chainsaw (I have it on 360 and it was fun)
I do not. PS4 is now the only Nintendo, Sega, Microsoft or Sony system I do not have (until PS5 and XSX release).