Hi,
There are two types of inverters. One is called pure sine wave--and will produce the same or sometimes even better power than you get by plugging into shore power.
The other type is a modified sine wave. It produces what are called square waves rather than sine waves--and that may cause "noise" on tv screens--and may cause computer power supplies to run hotter than normal.
The msw is cheaper. But good pure sine wave units of about 300 watts that will run what you want are not going to "break the bank", either.
Morningstar makes a wonderful small inverter. Go Power and Samlex also make quality units.
This is what is balanced and best for twin twelve volt batteries.
As it often doesn't cost a dime more to do this, I think it is worth the trouble.
If you wish to understand the "why" surf here:
correctly interconnecting multiple twelve volt batteriesOthers may say it doesn't matter--but unless there is a compelling reason to not optimize charging and discharging why not do it the best possible way?