A 1500 Watt inverter will run everything you want to run.
But the first thing you need to know is the amp hour requirements, in order to properly size the battery (or batteries). The battery needs to be sized so that the amp draws between fully recharging the battery doesn't discharge the battery down to below 50% Depth of Discharge. If you fail to properly size the battery, and undersize it, or fail to fully charge it when charging, or let it discharge down to the point where lights dim and inverters scream, the classic "no problems" of today turns into the classic "these batteries are a piece of crap" 18-24 months later.
Batteries don't die, their owners kill them.
That fridge is listed as 130 Watts, 1.6 amps. In reality it's less than that, more like .9 amps as the Watts will vary from 80-120 most of the time. But that .9 amps is at 120 volts. At 12 volts (120 volts divided by 12 volts = 10) it's 10 x.9 amp = 9.0 (+ 10% for inverter loss) = 9.9 amps per hour on the average. Depending on ambient temps and other factors it will run as low as 5 amps and as high as 16 amps, but about 10 amps overall.
Over the course of 10 hours, assuming nothing else whatsoever is connected to the batteries, that's 100 amp hours removed from the battery. To keep the Depth of Discharge to no more than 50%, you need at least a 200 aH battery bank. If you routinely run the battery down below 50%, the lifespan of the battery will be greatly reduced (a year or two rather than 6 or 7 years, for an AGM or true deep cycle battery, like golf cart batteries). Marine deep cycle batteries are not the batteries for running a fridge. You can do it, but they won't last much more than 18 months.
