Never owned or even played PS4 or a Vita will skip ranking them. Played but never owned a PSP and PS1.
Best games PS3 > PS1 > PS2 > PS5 > PSP
Best controller: PS5 > PS3 > PS2 > PS1 >PSP
Coolness factor (yes it is a real thing) PSP > PS2 > PS3 > PS1 > PS5
Additional features: PS5 > PSP > PS3 > PS2 > PS1 ---- honorable last place for PS4 since the sole reason I never bought one was the lack of 4K blu-ray support.
RE4 playability PS5 >>> PS3 > PS2 >>>> PSP >>>>>>>>>>PS1

Final personal ranking PS3 > PS5 > PS2 > PS1 > PSP
If the PS5 was a cooler system it would have won. But for its time I liked PS3 just a bit more compared to how much I like PS5 today.

Not taking backwards compatibility into account, PS1 has my favourite selection of games, so that gets my vote.

As much as I want to go against the grain and not say PS2.

It is definitely the PS2.

It got me addicted to many franchises in gaming, and even as I try out new franchises, a lot of them had their start or had a big boost in the PS2 era. Now of course I have a lot more money now compared to when I was younger so I am playing PS4 and PS5 a lot more than PS2. But I can't deny the impact of the PS2s games. In fact without the PS2, I might've been all in PC by now instead of the delicate balance I have now.

The thread results so far in the voting are pretty much what I expected.
1. PS2 - 14
2. PS4 - 12
3. PS1 - 6
4. PS3 - 5
5. PS5 - 2
No votes for the portables. I expected maybe 1 vote for each, maybe.
PS2 and PS4 battle it out in most voting for the top PlayStation. They both sold a ton (and PS5 is selling a ton and you can play virtually every PS4 game on it) and have highly acclaimed libraries. PS3 crapped the bed early on and some of its third-party games run worse than Xbox 360 so I'm not surprised it's not in the Top 2 PlayStation consoles.

PS5 of course, because it's the most capable. It's not even a question, is it?
Which of them got the best games relatively speaking, now that's a completely different question.

PS4 has the best games but with the question phrased like that its hard not to argue that the PS5 is "better" since it can play those games and more, while the PS4 had no backwards compatability. So I'd be very suprised if the PS5 ends up having the exclusives, but you could still call it the best system. Except when it comes to fitting in a normally sized TV cabinet.

Ps2 by a mile

That's not how the question was meant. A gaming system is a means to play games, so for many, perhaps even for most, the best system is the one with the best games.

Games make a console. Otherwise, it's useless.