Double action in revolvers, basicaly is a long, somewhat stiffer trigger pull that cocks , revolves and fires the revolver. Most double action revolvers will fire single action too(But not all).
Single action revolvers, and double action revolvers fired single action; the revolvers hammer is manually cocked, a light(er) pull on the trigger fires the gun.
The deal can get strange on semi-autos. A DA semi-auto generaly means a pull on the trigger cocks and fires the pistol, however subsequent shots will be single action as the slide recocks and reloads the pistol automaticaly.
A single action semi-auto must have the hammer cocked to fire, pistol will fire and reload and recock irtself.
Then there is the Glocks and clones, and DA only semi-autos, other striker fired autos, various mixes of the basic operating system. Most of these pistols cock themselves when you chamber a round, some partialy cock, and trigger cock when fired like a DA.
The key to any of them is the trigger. Learn your basic gun safty rules, they will apply to about any firearm, long or short.
Ask about any of the firearms you shoot, and learn the function and operation of it. I've been shooting various long and short guns for years and still have questions about function and safe use!
Be careful, the trigger is the key, no finger on the trigger, and gun is was less likely to fire. Learn the individual guns, many types and styles still in use, and invented daily.
If your new, best bet is to start with a DA revolver. But any handgun will do if you obey the safty rules.
Buy quality handguns! Junk is fine for occasional use, but if it don't work it don't work. Buy quality firearms and you will be much happier in the longrun.