I still have a very basic back-up system at home, it's something I installed a few years ago when we were have power outages of 3-4 hour duration on alternate days.
Firstly forget halogen lighting of any kind, they're a fire hazard, they're fillament so they're unreliable and they're extremely innefficient. Use LED lights.
Secondly forget car batteries or any normal lead acid batteries, they're not designed to be discharged by more than 20%, discharging them more than that destroys them in no time (<a month) You have to use deep cycle lead acid batteries, yes they're more expensive but they should last years rather than days.
Because we were getting the power back on every day solar wasn't worth the extra expense. The cheapest route for me was a small, cheap 5kVA inverter that was plugged into the normal supply and 4x lead acid 110Ah deep cycle batteries to provide back-up power. .
The inverter ran all the important items in the house such as 3x PC's, 1x server, ADSL router, cordless telephones, TV, satelite decoder, Hi-Fi system, as well as occasional use of microwave, kettle and coffee machine. On batteries it would run for around 5 hours with everything on and about 7 hours if I shut things down when I wasn't using them.
I also installed some 12vDC LED lighting around the house, it was mostly cheap 10 watt floodlights and some adhesive tape type lights. Obviously the lights ran directly off the batteries, not from the inverter.
