You will find some people who greatly prefer plasma, and others who love LCD. The two are much closer, quality-wise, than they used to be so in general I don't think there's a huge advantage to getting one over the other. For me, the most important factor was the picture quality and I think the best way to see what you prefer is to look at the different types. I would recommend spending some time looking at display TVs without looking to see which type they are, and choose your favorites. (Keep in mind that different stores might set their screens differently - some places they'll be brighter, some dimmer, etc. so you might want to check the displays in several different stores if possible.) When we did that, we discovered we had a very strong preference for LCD - every one of our favorites was an LCD, and all of those we disliked were plasma. LEDs are newer and look really good, though they were significantly more expensive when we were shopping for ours so we ruled them out. Their prices might be more in line with LCD and Plasma by now.
I'd recommend getting 1080p rather than 720p, assuming you are getting a large screen. I'd also suggest a minimun refresh rate of 120 Hz. Some people swear by 240 Hz, and my TV will do that, but I honestly don't see much difference. (In fact on some things the 240 actually looks a little odd or unnatural, for some reason.)
I have a Samsung and I love it - I would highly recommend that brand and I think they are usually very highly rated.