Lots of good reading at the site Chuck mentioned.
I have a single battery bank that powers both the DC circuit and the AC circuit. I have 4 x Trojan L16H batteries, rated at 420 AH each @ 6 volts. They are wired in series/parallel to make a 12 volt system. A fat wire goes to a 600-watt inverter, another fat wire goes to a DC switch panel.
It's important to have some sort of instrumentation to keep an eye on your battery bank's health and state of charge. I use a Tri-metric 2020 but there are lots of options.
Do you know how often you'll be on shore power? That will help determine the size of your battery bank, and also the number of solar panels if you go that route. The first step down that road is to quantify your power needs. Make a list of DC and AC appliances and loads, and the amount of time they'll be going, and you should end up with a good idea of what your daily power requirements are. Be sure to account for different power usage on weekdays and week end days; take the higher of the two numbers. The final number should be in watt-hours per day. Depending on how much autonomy you want, this will help determine the size of your battery bank. The AC load should give you a starting point for sizing an inverter, but bear in mind that AC motors have a startup surge that requires more juice than normal running (food processors, power tools, etc.).
Using the max possible load you may encounter on either the AC circuit or the DC circuit, you can size the wires needed to run from the battery bank to the inverter and DC switch panel. The distance between the battery bank and inverter & DC switch panel also factors in to wire-sizing. There are tables on the web and elsewhere that will tell you the correct wire size to use for carrying x current over y feet.
If you do your power calcs using a spreadsheet program, you can easily see how power requirements are changed by removing certain things, like a DC fridge or a hot pot, or using a laptop vs. a desktop computer.
Hope this helps -- good luck.
PS: I'm not sure what a solar fridge is -- any electric fridge can be powered by a battery bank. There are efficient DC fridges that are made for off-grid use. They cost a lot more than a dorm fridge from Sears, but use a lot less power. If you are going to be using shore power, then there is no question that a standard fridge will cost less than a DC fridge and the requisite solar panels, battery power, wires, etc. If you need to be away from grid power for any period of time, then it may be time to start doing calculations about fridge efficiency, power consumption, and battery & solar panel requirements. If you are only going to be off-grid for a few days at a time, it may be better to simply buy bagged ice and keep your perishables in cooler(s). The price of an efficient DC fridge, panels, batteries, wires, etc can buy a lot of ice.
Here's the page on our fridge install: http://seanf.smugmug.com/gallery/1308951_2Ni8k