OK, lots of choices here.
First, the campground outlets are two basic styles - 30 amp and 50 amp. The 30 amp is one round pin and two angled blades, is 120 volts, and provides (30x120) 3600 watts. The 50 amp is one round pin and 3 parallel flat blades, is 240 volts, and provides 12,000 watts. Most household outlets are 20 amps, maximum, and are usually wired with the common-looking 15-amp outlets. (True 20-amp plugs have one blade turned 90°, and the outlets have one slot and one "T" shaped hole. The different blade styles are to keep people from plugging heavy-duty appliances into light-duty wiring.)
If you are going to be plugging in to houses, etc. keep your load down to 2400 watts, or 20 amps. Use a 12-3 or larger shoreline cord for 20-amp capacity, with a standard 15-amp plug on the business end. For about $5, you can get a hockey puck that plugs into a 30-amp campground outlet, and plug your standard plug in the back. I ditched the 30-amp cord for our lightweight trailer to save weight, installed 20-amp wiring to the "mouse hole," and threw a hockey puck in the cabinet. I usually only plug in in the driveway, but can toss a heavy-duty outdoor extension cord in if I think there will be an opportunity to use it.
The one vanguy67 shows is the complement, the one you want is this one: http://hardware.hardwarestore.com/30...er-668438.aspx
To charge the batteries, you can go with a battery charger, an RV 'converter,' or an inverter/charger all-in-one. A 'converter' is a power supply that is designed to power 12-volt loads in an RV with or without a battery connected, and charge a battery if it is there. Don't try to power 12-volt loads from a battery charger with no battery connected. The chargers have little or no filtering, they depend on the battery to stabilize the voltages.
The simplest way to switch power is with a plug. If you put an outlet powered by the shoreline next to the inverter, and bring your internal wiring back to a plug, move the plug to switch from shore power to inverter and back. Many home-brew generator installs have a generator outlet and a shore outlet next to each other for a keep-it-simple-stupid foolproof system. You can also use manual or automatic switch gear, but your question is a little to broad to get specific on that.
I would advise against powering all 120-volt loads on the inverter when shore power is available and charging the batteries. Unless it's critical and can't be interrupted, like medical or satellite equipment, switch the 120-volt load to the shoreline if it's adequate. The losses in converting the shore power to 12 volts and back to 120 volts will waste some of that electricity, and you will miss the opportunity to give your inverter a rest.