Which type of screen will provide good video quality for PSX/PS2?

I tried to become accustomed to very blurred and ugly graphics on PSX/PS2 plugged into my TV with a big screen, but it depriving me of any enjoyment of playing games. So I'm wondering which type of TV or monitor special dedicated for this old Sony's consoles. Generally, the most interesting option for me is an LCD monitor/TV with about 20 inches diagonal screen, but I am not sure if an LCD monitor/TV will behave differently than a big TV OLED, which kills all the fun in the game. Does it make sense to prepare a gaming station with the LCD monitor, or am I convicted of old, heavy, and ugly CRT TV?

If some of you will confirm, that LCD variants can handle video playback in acceptable quality, the next question is about preferred inputs available in devices. Most of the LCD monitors with mentioned dimensions have just VGA and DVI inputs, so I am a little afraid about quality loss due to converters from VGA to SCART/RCA. However, this problem with converters does not exist in the case of the LCD TV or LCD-TV-monitor hybrids, because as I can imagine, they have these inputs.