Pretty much any TV from this century.
The TX-SR605 has S-Video and Composite Video and analog audio for very old devices (TVs).
It comes with Component Video for no so new devices.
And HDMI with digital audio (optical) for the latest TVs
TX-SR605 is compatible to almost any TV you can find.
The catch is, you can not pass any 4k signal from any source to the TV via TX-SR605.
I would consider replacing your TX-SR605, if you plan to go 4k.
You can use any TV that has a digital audio output which is basically just about all.
Connect all your video sources directly to the TV.
Connect the digital audio output of the TV to the receiver.
Check the TV manual on how turn on the digital output. You may also have to turn the TV speakers off.
Check the AVR manual as you may have to assign the digital input to an input name.