Making a Solar Power Battery Backup Unit
You have the basic concept down.  Your challenge will be sizing.


What's the minimum possible load you can put on the system?  For instance, don't use an inverter to run lighting.  Run the lighting direct off 12V, and there's a huge variety of 12 volt LED lighting: from screw-in bulbs, spot or flood lights, LED strips that let you freestyle your lighting, etc.  No problem getting iPad chargers for 12v, every gas station has them. A surprising number of internet routers and TVs will also run on 12V directly (partly, this is for campers).
Inverters are not efficient. Put every load you possibly can on 12 volts direct. Simply at idle, with no load at all, it consumes 12-15 watts, or all the power your solar panel makes on an average sunny day.  Obviously you only want to run it only when absolutely necessary for loads you can't get in 12v versions.
It is usually cheaper to make loads efficient than to make your system bigger to handle inefficiency. 
If it's forgotten and left on, put it on a timing mechanism. 
Once you have your loads down to practical minimums, you can think about sizing the battery and solar panel for your loads. 
Make your battery's amp-hours 3-4 times bigger than your expected load.  If you "bottom" a lead-acid battery regularly, you will greatly shorten its life.  It's unfair but true.
Size your battery for your "burst" usage, i.e. so it can make it through your hardest day's usage, and so typical days' usage use less than 30% of its capacity.  
"Battery protectors" are readily available, the best are probably those which disconnect your car's battery while it still has enough juice to start your car.   The solar panel (charger) should go straight to the battery (fused of course).
Size your solar panel to fully recharge your battery in between uses. 
How many days can the system function with no usable sun? (how often will this happen?)
How quickly will it recover from a deeply run down battery? 
Fuse everything, to protect your wires and battery from catching fire or taking damage.  


It really all depends on your situation.  I have an application with a fairly large battery (about 300 pounds, NiFe) that burns a 60 watt spotlight for 3-6 hours a weekend, then has all week to recharge.  A 20 watt panel is plenty, even when laid horizontal and covered with plexiglas and dirt.