Just be aware that the reason for a fridge being A+++ may be partly because its got such thick insulation, so you may get less space for food inside than a lower rated one! We run a Neff 240V fridge with no problems whatsoever. The fridge motor draws sufficient power to take the inverter out of standby mode, although the interior light doesn't, and will flash every few seconds if the compressor's off. Our 240V fridge takes an average of 1.75 Amps (measured over 9 hours at night, with no other electrical equipment on).
Also be aware that a TV in standby mode may take sufficient power to keep the inverter running, so make sure you switch off at the socket when not using it. I've checked our TV power consumption and it takes around 44W when on (approximately 4.5 Amps at 12V) - this is a modern 32" flat screen LED TV. The one that came with the boat (same screen size) was an earlier model, not LED technology, and took 4 times as much current and really hammered the batteries! Check the rating panel when you buy one.
If you have electronic equipment that will run off a 12V external supply, or has an internal 12V power supply, and is not specifically designed to run off a lead-acid battery, you will probably need to stabilise your battery voltage, as 14.4 volts could be too much for the equipment. Bedazzled sell a couple of 12V-12V stabilisers for LED strips, to avoid flickering and overheating, but when I asked they recommended the larger of the two as being more suitable for supplying other electronic equipment, as it provided a more stable output. Their actual words were:
I wouldn't recommend the smaller LVDC24W due to its performance under varying loads however the larger LVDC60W is ideal for anything 12v and (obviously) up to 60W. In fact this power supply is a variant of a range designed to supply power to Televisions and Laptop computers and hence is very suitable for anything on 12v