I have an 800 w inverter from camping days..used in kombi to run 220 fridge when travelling. And various gewone battery charges. What else is needed?
Just a battery.
A car invert would run on 12vdc (not 24vdc), so that means you'll only need one battery. But as it depends on the cars alternator to charge the battery, and does not have a build in MPPT charger. You'll also need one of your 'gewone'

chargers.. make sure to use one that supports trickle charge (to keep the battery topped up, deep cycle batteries are best stored at +90% charge).
For the battery, try http: // zulteck.co.za /... I bought my Royal 102AH for just under R1000 from them (Good batteries). Of course you might be able to get away with a smaller (/cheaper) battery based on your equipment's load. PS when doing choosing your battery make sure you get a battery with double your load requirements... deep cycles also do not like to being drained beyond 50%...
i.e. if your equipment uses 400W/h (tv+dish+amp+dvd player) and you need to run it for 4 hours (total 1600W)... as roughly a 102AH @12vdc battery gives a thumb-suck 1200W you'd would need 3 of them in series...
There all sort of fancy thing you could do with simple 12V automotive relays to do automagic switching between putting current into the batteries via your charger when the power is on and to the invert when the power is off...
i.e.
Battery + = common
Charge + = NO
Invert + = NC
Use the chargers 12V to close the relay when you have power... disconnecting the invert and starting the recharge of the battery.
PM me and I'll draw you a diagram.
Or even... Buying a cheap 20A solar MPPT charger (R200) with a 85W panel (R850)... and permanently run your TV off-grid... etc, etc, etc