the question is 2 fold. what connections does the LCD panel you're looking at take as well as what connections does your device put out.
These days, if an lcd panel is called a TELEVISION, it most likely has HDMI, VGA or DVI, Component, & Composite. They will also have built in speakers and a tuner. It will also have a Slower response time, usually 5-7ms. These connections cover the multitude of what is put out by most players.
Old technology like VCR will almost always be Composite/S-video & possibly component video.
Combo DVD/VCR will have the same as VCR, but newer models may put out HDMI. Especially if your device has built-in upscaling.
All blue-ray players will support HDMI, some will have component connections, i doubt any of them will support lower than component connections.
One thing you may want to check, is the resolution on the LCD panel you're going to get. If you're going to spend time on BlueRay, you might as well make sure youre LCD accepts at least 720P(1280x720), but 1080p (1920x1080) would be better. you would probably not notice the difference between 720p and 1080p on a screen that small though.
So in closing, what you want to do, is check the INPUTS on the LCD TV you're looking at, and make sure the device (dvd/vcr/BR) has the same type of OUTPUT.