Robert,
There are three kinds of inverter that you can buy:
Square Wave output: This output is simply 120 volt dc that changes polarity 120 times a second. It works just fine in AC/DC loads such as some electric motors, heaters, and some electronics. Some loads it will blow up. You don't see these much anymore.
Modified Sine Wave output: This output is around 145 volt dc that also changes polarity 120 times a second, but is "off" for a couple of milliseconds at each change. This is much easier on motors and transformers, and will run most stuff. It may not work on sensitive loads such as audio electronics, and won't run some computer power supplies. May interfere with radios.
Sine Wave, or True Sine Wave: Same stuff as what comes out of the wall at home, a smoothly-changing voltage that peaks at almost 170 volts. It is lighter (less copper and iron) and works on anything.
An inverter/charger contains the inverter, a transfer switch, and a battery charger. This is great because you will need the switch and charger anyway. You may already have a good charger, and you might be happy with a manual switch, your choice.
You have 30 A / 3600W available through your shore-power hookup, but you may not need all that away from the dock. Every ac amp you draw costs 10 or more dc amps from the battery. Don't try to heat water or some such from your batteries!
Jeff is right about cost.
You won't often see square wave output these days, just as well. Don't buy one even if it's free.
Modified Sine Wave output has been around for a while (I designed one for use on Medevac helicopters back during the Vietnam war) and are cheap, as Jeff mentions. You can get a 3KW inverter for $200, see ebay item # 120306810733. You can get a 3KW inverter/charger for less than $900, see ebay item # 220341088087.
Sine Wave inverters are newer and more expensive. A good 3kw inverter/charger, Xantrex's newest, can be had for $1700 or so, see ebay item # 270228321887, and an AIMS brand inverter-only for less than $900.
Fastjeff seems happy with a modified sinewave unit, and I don't think I would spend the money on pure sine wave unless you needed to run a plasma TV or some other fussy load. Even electric burners with electronic control seem to be happy with the modified sine wave.
1975 32' Flybridge Sedan, twin Perkins 6-354 diesels, 1:1.53 velvetdrives, 16 X 19 props. Merritt Island, Florida