There are many different sizes and designs of lead-acid batteries, but the most important designation is that they are deep cycle batteries. Most solar power systems generate DC current which is stored in batteries. Then it is transformed, filtered, stepped, etc. to get it to an acceptable output waveform. The more processing, the cleaner and quieter the output, but the lower the efficiency of the conversion. The goal becomes to produce a waveform that is acceptable to all loads without sacrificing too much power into the conversion process.
Inverters come in two basic output designs - sine wave and modified sine wave.
Most 120VAC devices can use the modified sine wave, but there are some notable exceptions. Motors and power supplies usually run warmer and less efficiently on mod-sine wave power. Some things, like fans, amplifiers, and cheap fluorescent lights, give off an audible buzz on modified sine wave power. However, modified sine wave inverters make the conversion from DC to AC very efficiently. They are relatively inexpensive, and many of the electrical devices we use every day work fine on them.