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If it were my money, I'd be looking at the LH3000. It's a better TV than the 2000. It has a better panel with better colour reproduction than the 2000. It's also full HD 1080p which, although not essential for SD TV viewing, you might wish to upgrade at a later date, buy a Blu-ray player or use your Xbox to upscale DVD to 1080 resolution. If you are going for a TV larger than 32", consider a full HD panel.
The 3000 also has three HDMI inputs, as opposed to 2 on the 2000 model. The more the merrier in today's digital world.
The 3000 also has the intelligent sensor - a nice little set it and forget it feature that is useful if you don't wish to calibrate every input of your TV to a set standard. I use the sensor for normal TV viewing and when playing the odd game on a console.
If your budget can stretch to it, the 3000 is the one to go for.
For just TV? Yeah, I guess the 2000 is good enough. It's the LCD equivalent of the TV's we had 10 years ago, except with higher resolution and up to date connections.
If you think you'll never use the TV for more than you say, I can't really see a reason for not going for it. If you see yourself wanting more from a TV in the future, the little extras on the 3000 will help you out.
The LF2510 is only better than the 2000 by having a full HD panel, and that really is the main difference. There really is very little info about the lf2510 for two main reasons. 1. It is based on an older model, possibly as early as 2008, maybe an LG3000. Not bad, but not up to date.
Reason 2. the 2510 was/is intended for the European mainland, and most any info on it is not in English. Chances are, it is available here as 'cheap' import, helping the retailers to increase their profit margin on this TV.
As you say, it is smack bang in the middle of the LH2000 and LH3000. I can't really add more to it. You could quite easily go round in circles with these three TV's.