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A 300 watt inverter should run the lot. At a pinch, you might just get them both running off a 150 watt. A quick Google suggests that a larger LCD TV uses 80-120 watts. I doubt the Playstation will use much at all. Both should have a rating plate - if they specify amps and volts rather than watts, then just multiply the amps by the volts to get the wattage.
I'm not sure about LCD, but I've known CRT TVs to dislike the power output of the cheap 'modified sine' inverters. You might have to go for a true sine inverter, and they're considerably more expensive.
IIRC, Aldi are doing a 'cheap as chips' inverter at the moment (about 15 quid.) It might be worth buying one and just seeing if it works.
Currently in Horatio's garage:
2010 Laguna III Initiale.