Most if not all TVs (even no-name ones) are at least 60hz. True 120hz TVs however are still very rare, majority of the ones that advertises themselves are doing it via interpolation or black frame insertion.
Yes, 30 and 60fps is very noticeably difference.
I've been playing on 144hz for 2 years now, switching to 120, 60 and 30 throughout this period as well.
My experience are (in as layman terms as possible) as follows:
30 to 60hz = Day and night difference, instantly noticeable. You gotta be brain dead not to notice it.
60 to 72/75hz = Subtle difference, it's the cheap-man's version of trying to get more hz.
60 to 90hz = Quite noticeable, but not a day and night jumb.
60 to 120hz = A day and night difference, equivalent to jumping from 30 to 60hz.
60 to 144hz = Pretty much like jumping to 120hz, except with even less input latency. I'm not a pro SF/GG/BB fighter where I can count buffers and latency with my eyes so I can't appreciate the improved latency.
*bonus
120hz to 144hz = I can't tell the difference. For me, 120hz is where the diminishing returns kick in.
120hz to 165hz = I haven't played enough on 165hz, so I do not have a conclusion on it yet.
Now understand that up to 60hz, everything else only applies to PC gaming. Consoles are locked to 60hz and will forever be locked there unless everyone can stop whining about the possibility of $1,000 gaming consoles and TVs that cost half their myvis.
Get a good 4k TV that does HDR properly (both Dolby Vision and meta HDR10), a TV that upscales content well, and a TV with low input lag. That's about all a console gamer needs.
*EDIT*
However, with the advent of HDMI 2.1 - variable refresh rate can be a real game changer for console gaming.
If implemented correctly, the next-gen consoles can in theory give console gamers a smooth gaming experience regardless of the framerate (up to 60hz however) with no screen tearing and minimal input lag. Think Gsync/Freesync, but at a more moderate level. It's really the next most important thing for gaming.
Resogun. Native 4k, 60fps.
inb4 "
b-bu-but it's not AAA game!"

Ben, would like to ask you something considering you are very knowledgeable.
I am planning to change the HDMI cable for my PS4 Pro as the default is too short, does the quality of HDMI cables matter?
I see some HDMI cables are 2.0, some 1.4, and some really expensive ones.
Did my research and some sites say that it doesnt really matter what HDMI cable you use, it's all the same?