The garden variety lead acid batteries I grew up with are apparently refered to as "flooded", meaning that you can remove caps and add water or sample the electrolyte as you feel the need. Batteries intended for starting cars are optimized for high current output and are expected to remain in a nearly fully charged state. Your typical car battery has about a 60 amp-hour capacity, but this can vary from 40 to over 100 amp-hours, or even more widely.
So called "deep cycle" batteries have an internal construction that endures repeated cycling between being fully charged and nearly fully discharged, they may not deliver as much current for operating a car starter.
There are also sealed lead acid batteries. These are intended for applications where the battery may operate in various orientations (including upside down).
It is not harmful to connect a discharged battery to a higher charging voltage (this is known as bulk charging). It will speed up the charging process (too much though will probably overheat and damage the battery), the excess voltage being consumed by the charging process. The trick though is detecting when the battery reaches full charge.
When a voltage above 2.35 volts per cell is supplied to a full charged battery, electrolysis of the water in the battery takes place producing hydrogen and oxygen. These gases are explosive, and will produce a hazard if not vented. In addition, electrolysis consumes water in the battery. This is a serious problem for a sealed battery. Water lost from a flooded battery can be replaced, as long as the loss is detected and remedied before damage takes place.
A charging voltage of 14.7 volts would be a good choice for bulk charging, as long as it was reduced to a "float charging" rate as soon as the batteries are fully charged. A good float charging voltage would be 13.5 to 13.8 volts, and there would be no harm in keeping a fully charged battery connected to such a voltage.
Lead Acid battery charging (for flooded batteries) has a coulometric efficiency of about 70 percent. This means you must inject 142 amp-hours to get 100 amp-hours of charge. Sealed lead acid batteries have a significantly higher efficiency, even 95 percent is not unusual.
Tom's notes / firstname.lastname@example.org