Component is said to only go up to 1080p - however, most of the time this isn't the case, and the 1080p is worse quality, so it's typically dumbed down to 720p or 1080i. Also many HDTV's or media playing devices will not allow you to achieve 1080p or 1080i over component cables. Not to mention you get a nice mess of wires at the back of your TV. Composite is also worse than component, but only has 3 instead of 5 wires. HDMI is a single wire, typically thin. It boosts your resolution up to 1080p, so true HD quality. It also supports TRUE HD 5.1, 6.1 and 7.1 surround sound. Component only supports up to 5.1, but you will notice an inferior audio. Seeing as you have 42" HDTV (Most likely LCD in this case) you have a large screen to fill. Now, Component or Composite cables will look worse on larger screens, due to being stretched more. HDMI will fill the frame much better, without loosing quality. I'm actually confused as to why the 42" LCD HDTV at 1080p doesn't have HDMI, especially if it's by LG. Now, yes, in all HDMI cables are superior in the terms of gaming, TV viewing, audio, and movies! You will be able to tell the difference. In my personal opinion, I wouldn't settle with a 20-24" TV just to support HDMI and 1080p. Unless your in a smaller room, and up closer to the TV. However, if your further back, and the room is more spacious, then I suggest something past 34". 30" range is nice in smaller rooms, and sometimes slightly larger rooms, but I suggest a 42"-47". Save your money. If you want to make a bold move, and can take care of a TV, buy a high quality brand-name Plasma TV in 1080p. Something like a Sony, Panasonic, or a Samsung typically hold up strong and true. If not, a brand-name LCD will offer typically better viewing angles, better visuals, and better sound. TYPICALLY! But all in all - HDMI is vastly superior to component, especially if you have surround sound, or a larger screen... Or both!
Long time in the field of audio, visuals, gaming, PC customization, TV's, DVD's, Blu-rays, and Home Theatre. Trial and error is also your friend!