I've been using a "small" system for several years now Spam. I'm going to be upgrading the system from a 150-200 watt 24v battery/inverter system (510 AH of battery storage for inverter). To a 1 kw system with a "grid tie" inverter added so that I can also "net meter" back to the "grid" (run the meter backward when producing more than I use).
The Basic system you describe should be fine for your needs starting out in order to run small, low-current devices "experimentally" just to see what you would really want or need the system to do.
As advised, a PV system is not efficient at running high load items like resistive space heaters or water heaters.
As spring is not too far away now, lets say you want to have back-up or emergency lighting, either LED or DC or AC fluorescent lights.
Here's your list...
Panel: a 10w 12v panel would give you about 2.5 amp/hrs per day if you had 5 hours sun exposure (more of course with more sun). I used the figure from a 10watt Solarex panel.
Battery: Important note here!!! Lead acid batteries( the type most used for storage) "Deep Cycle" or not... DO NOT like to be discharged completely!!! 50% is about the max. and 30% is even better if you want to get the most life out of them. Properly used and maintained, batteries will last quite a long time
.
So for lighting for example, what I would do for a 10 watt panel(figure about 8 watts in actual use, panels are usually rated at 1000 watts per sq. meter of area which is good for the Sahara desert on a sunny day, but not say the midwest :blink
, is to get a battery of twice that size so that using 2.5 amp/hrs wouldn't take it down below 50% of capacity, and the panel (at 5 hours of sun) could "put back" that 2.5 amp hours the next day...
For a system like this you would not need a "Charge Controller" since the Panel would not be capable of overcharging the battery, because of the limited panel current and because the panel current will also reduce as the battery voltage rises at the end of charge.
Inverter: for applications where you would need an inverter to provide AC from DC input there are some things to consider first...
Quality of AC output: some some electrical devices are "fussy" and need a "clean" AC sine wave, some don't care at all, and some will "run" but you can tell that they would rather have the "really good stuff". So Inverters come basically in three "flavors"...
"square wave": basically the cheapest small ones, instead of a smooth sine wave the output just goes positive for a half cycle, then negative for the other half cycle. The Inverters in the "middle" give you a basic "sine wave shape" of the voltage output, but its made of little "digital steps", but works fine for some things. The last category are the "pure sine wave" which the "steps" are filtered to give a basically the same output as comes from the wall plug (only without the noise spikes and voltages variations...).
If I go any farther this is going to become a "Novelette"... but hope it explains a bit