I've had good luck over the years with Samlex pure sine inverters, including their 300 watt. It comes with a cig. lighter plug, but like you say, S. Hank, you're introducing other limiting factors that way. It's best to install it close to your batteries (always, always keep the 12v run as short as possible) and hardwire it. If you need to use a 120v extension cord then so be it.
As far as how many solar panels goes, I don't understand the question. You mean people are hooking stuff up directly to solar without batteries to act as a middle man? Ya learn something new every day. With the miracle of batteries it doesn't matter how much solar you have. As long as your house batteries have enough juice (50 amps like MrMom said) then you're good to go. Now how long it takes for the house batteries to recover depends on how much solar you have (for someone like me who also hates generators and tries to get by on 100% solar) or shore power or alternator.