If I'm running an emulator, I don't like to use any filters but when it comes to the actual console, I would love to pick up a CRT. Maybe a Sony Wega 27", or a Sony Trinitron. Those are supposed to be really good quality CRTs. In my experience with older games on LCDs, I find that the games just look worse. They're stretched out and the colors seem off.
1. I personally like using filters. Even if it's just a simple 2x filter. I use NTSC filters most of the time.
2. Games DO look worse on LCDs, LCDs usually have poor black levels, poor color accuracy on average. Not to mention panel response time can make the pictures even blurrier in motion. If you get an LCD, look for one that has been shown to have excellent color accuracy and black levels. (Better yet get a Plasma, it's about as close to CRT level blacks and color accuracy as you can get. But if you have to have an LCD, look for one specifically with an IPS or S-IPS panel. I've got an LG with an S-IPS panel. Color accuracy is very good, even if black levels are on the light side)
LCD TVs though in general. Most have a panel resolution of 1920x1080. That's 2,073,600 pixels. And if you have an old games console. And you are using Composite, you are most likely sending it a poor 240p (320x240) signal(And that's even if the LCD supports 240p. Many don't) Which is only 76,800 pixels. Only 3% the resolution of a 1080p TV.
LCD's don't usually handle non-native resolution like CRTs do. And going to extremes like 240p/480i are going to present an extremely poor result almost 100% of the time without a scaler(480p can be ok). Most internal LCD scalers have problems with just scaling 720p to 1080p(Which can result in even MORE input latency)
The other advantage that CRT monitors held over LCD screens is the ability to easily scale to various resolutions. This is referred to as multisync by the industry. By adjusting the electron beam in the tube, the screen can easily be adjusted downward to lower resolutions while keeping the picture clarity intact.
The most notable disadvantage to LCD screens is their fixed or native resolution. An LCD screen can only display the number of pixels in its matrix and no more or less. It can display a lower resolution in one of two ways. Using only a fraction of the total pixels on the display or through extrapolation. Extrapolation is a method whereby the monitor blends multiple pixels together to simulate a single smaller pixel. This can often lead to a blurry or fuzzy image particularly with text when running the screen below is native resolution.