I agree with the comments mentioned regarding power supplies. Many smaller TVs receive power from a power supply which plugs into 110V. Plugging direct from your 12V batteries into the TV will be so much better for your battery(s). The other advantage is that you can watch TV anytime, with or without 110V power. I would pick a TV that operates within a couple volts of 12V. I seen a few TV power supplies that generate 19V so I am not sure how well they will operate in the 12V range. If you love such a TV, I would buy it, then try it and see.
One other point to note is the wattage of the power supply. The lower the wattage, the less power it needs to operate. This means your house batteries last longer between charges.
For the record, here is what some power supplies look like, common on the smaller TVs. I think 32" is about the limit, most popular in the 24"-28" sizes