Firstly a large deep discharge battery is the
way to go. Sam's sells deep discharge/cranking
batties (which weigh 50 #) and I have used them
for all sorts of things. Powering a home
made inverter, a trolling motor, a tractor and
finally a AP400 mount.

Of course this only works if you are a weight lifter.

Size matters.

Secondly a spike current on any battery is going
to drop the voltage.

There are three ways to get around that:

1. isolate by using a separate battery
(already mentioned).

2. Use a 12 volt DC to 120 volt AC converter.

I believe that the current crop of inverters
has a DC to DC converter followed by a DC to
AC converter. I suspect that the DC to DC
converter regulated the voltage.

With or without a 120 volt to 12 volt DC
switching converter (the type that radio shack
sells).

While somewhat less efficient you should
have very regulated voltage using this.
You should be isolated from any transient
battery effects.

Of course the 12 to 120 volt inverters
typically drop out at 10 volts.

3. An isolation diode and a big capacitor
or small battery.

The big capacitor might be one of those
things they use for car audio systems so that
the load from the audio system doesn't reset
the car computer.