Hey, a charge controller is good to have, especially if your panel is larger or if your climate is sunny - it prevents the battery from overcharging and also indicates low battery status. There are a ton of websites about this topic.
For just the light with low wattage and a small panel, I started without a charge controller, it worked just fine. (but now I have one, because I upgraded the panel to 150w and expanded my setup to now include a battery bank to also run a heat lamp and christmas lights).
The car inverter will have the cigarette lighter male end, which screws open and you can jam a wire in the tip. THE TIP OF THE CIGARETTE PLUG IS THE POSITIVE END + and connects to the positive battery lead.
The sidewalls are negative (ground) and connect to the minus pole of your battery. You can just bend a wire around it and connect to the negative.
Recommendation: try and really isolate those wires, using electrical tape, soldering or what have you, since a short circuit between battery poles can heat up quickly and let the sparks fly.
In my initial setup, I did not have any fuses and monitored it very closely. Since then (in my involved version), I have added some resettable fuses in all the positive lines, for safety reasons.
Note: theoretically, another (simpler) way to make this whole thing work, without the inverter, is to just get 12v LED lights (or LED car lighting chain), however I could not find 12v timers anywhere (to me the timer was important, to control the light), which is why I went the 120v route (with the benefit that I now have extra power outlets for other things).
Another question was where I have all the stuff. Initially, I took a big rubbermaid box and put it all in there, with lid on top, just a few wires coming out. Since then, this has evolved too and its now in my garage, with the added benefit that the batteries are not out in the cold (decreases battery efficiency).
good luck!
If you are interested in the solar topic, I highly recommend some googling.
I really like jeffrey yagos solar 101 series, it starts here
http://www.backwoodshome.com/articles2/yago87.html