I have a NovaKool R5810 5.8 cu ft fridge, DC only. It draws about 4.5 amps while running, but it runs less than 50% of the time even on hot days. I figure I'm running around 35-50 Ahr per day during the summer. That is about 420 - 600 Whr.
You could feed that with a 85W - 150W solar panel so your 95W panel is a little small, given that you will have other loads.
I have 400W and a 220Ahr battery but that is probably overkill for most folks. I run all summer long, almost always without hookups, and I use my computer and a tablet for music (don't worry - I use headphones!) a lot. I also run an Engel 12V cooler (same type of compressor) for beer.
If you add another 95W panel you will likely be in good shape.