"KAH9158" A decent sized UPS would help even out the load and bridge over the sudden drops when another appliance comes on.
I personally use an APC Smart1400 UPS. It does all the normal power conditioning for low voltage sags and high voltage surges and when on battery backup, the "Smart" line of APC UPS's produces a true sine wave AC output. Many less expensive UPS models produce a "modified square wave" AC power when running on batteries. This is fine for computers with their switching power supplies, but can cause problems with equipment using transformers in the power supplies.
You would need to get the specifications on the equipment you want to power through a UPS. Most UPS's are rated in "volt-amps" (voltage times ampere current draw), most equipment is rated in "watts". In a quick and dirty way, "watts" = volt-amps multiplied by 0.70 Example 1000 voltamps = 700 watts (approximately).
Also, it is best if your UPS capacity is about twice what you think you need. This will give you some reserve "run time" on batteries and allow the bulbs in your RP TV to cool down some after you turn off the TV in a long power outage. (I'm assuming your TV will continue running a fan on the bulb(s) for a cool down phase after the TV is turned off).
I live in a rural area where the power supplied by the electric company will easily drop to 105 or 106 volts AC during the peak air conditioning times of the day and the APC Smart1400 will click on a voltage boost circuit to bring the output voltage back up to 115v. This is not running on batteries, it is still on normal AC power, it is just truly "conditioning" the AC power back to normal. When we lose power completely, the run-time on the batteries allows me to turn everything off in an orderly manner - so nothing has a "hard crash" when it loses power. My DishTV box is very suseptible to that. A UPS does need replacement batteries about every 2 to 3 years, so it is a cost you plan for.
www.refurbups.com