There is also a fellow over on this tread
who gutted a trailer to the frame and has built a system from the ground up. He's just about to put the solar in but weather and a bum knee has him on hold. Terry (Harley1994) might be willing to give you some advice since hes already done all the math. (Sorry Terry, I volunteered ya)
But here are some basics.
To start you have to get the numbers together for what your current draw will be for each of the things you want to run while off gridding. Then for the 110 stuff, you need to get an inverter that can run the right amount of current. Make sure you are looking at continuous output not peak and make sure the peak will give you some buffer for "starting" anything electric. A fridge has a short surge when it first comes on. So does AC or a fan motor.
You will need more than one battery unless you only plan to do very limited 110 volt stuff. Some of your juice is consumed by the inverter. Best route is four 6 volts wired in series or series/parallel to get either 12 or 24 volts. See photos.
A small flat panel TV like this one
is pretty light on current for a TV, I'm sure there are better.
Power Supply (Voltage, Hz) 100V ~ 240V, 50/60 Hz
Power Consumption Normal on: 33w. Sleepmode 1w. DC off 0.4w Standby Mode 0.4W
Your solar panel(s) needs to be able to produce in 10 hours more than you will consume in a day by 20%. This will give you some cushion and allow for some cloudy days.
As for your broken fridge, to make use of it without servicing/replacing, just pick up some dry ice on the way out of town and use it as an icebox. Just a thought. No point in it being dead space.
Hope this helps you at least get started.