HDTVs will vary greatly on how well they handle the signal from old SD consoles. My 7 year old Sony 720p rear-projector works pretty well with composite input, though has some issues with S-Video that I haven't been able to figure out. Very little lag. You can try googling various model numbers plus the keywords "input lag", but even then it can vary between inputs and numbers people will quote probably apply to HD inputs. It's a bit of a crapshoot.
I'd like to get a CRT for my retro gaming, but I keep putting it off because hey... a 27" tube is freaking heavy.
Keep in mind that old light gun games (the kind that make the screen flash) will not work at all on modern HDTVs. Aside from that, with the right HDTV and settings most retro stuff can look pretty good.