Re: Batteries for dry camping
First of all, make sure you have the 'best' batteries for dry camping, true deep cycle batteries. These will have only an AH (amp-hour) rating, no Cranking rating at all. If it has any cranking rating, it is less good for dry camping.
Next, decide on 12 volt or 6 volt. 2 6 volt batteries tend to be 'better' than 2 12 volt batteries, but may not fit as well (they tend to be taller', and MUST be used in pairs.
For 6 volt, you need pairs of them in series to make 12 volts, and you can have any number of pairs in parallel to provide longer service between charges. For 12 volt batteries, any number in parallel is acceptable. Note that all batteries should be as similar as possilbe (specs and age), because if not, they can 'fight' each other.
Under the sink is often not a good idea. You increase the odds of shorting them out by dropping something across the posts, which could lead to a fire. When charging batteries, you tend to produce hydrogen gas, which if not vented to the outside could explode. And frankly, batteries tend to get messy over time.
Your best way to power your TV is to use a TV which runs off of 12v directly. I had a nice RCA TV/VCR in my trailer which could be powered by either 12v or 120v. Run the batteries to a 'cigarette lighter' or '12 volt' outlet, and plug in the TV. If you don't want to get a new TV just to use 12v, an inverter can work. Smaller ones can plug into that 12v outlet, or bigger ones can be wired directly to the batteries. Note that most small and all cheap inverters produce 'dirty' power which can drive some TVs crazy. A 'True Sine Wave' inverter will work fine, but will cost a bunch.
For longest battery life, try not to discharge your batteries more than 50% before recharging.