Wait for OLED if you want that big jump like you ask for, trust me. Unless your current tv broke and you absolutely need to replace it, wait for OLED.
A good time to jump would be when next gen arrive, OLEDs keep getting better and cheaper each year.
Also HDMI 2.1 is coming (variable refresh rates), all current TV's will be outdated soon.
As for burn in, people need to learn the difference between burn in and image retention, what you get is the latter which disappears over time.
Plasmas were notorious for this as well, and people in the LCD/LED camp would recommend it over plasma because of "da burn in" which was dumb, because plasmas had superior image quality, and burn in wasn't a problem since the early 00s.
My 8 year old plasma has no burn in, and it went through hours of static images when I was afk at games or my PC that's hooked up to it.