The reason for the differences is because manufacturers aim to please (no pun intended). There is a huge, often volatile difference in opinion on what action type is the best. For example, Heckler & Koch simply gave up and offer their USP pistols with no less than 9 different action variations!
There are advantages and disadvantages to each trigger mode. A short single action trigger allows you to get the fastest, most accurate repeat shots. It is also the most likely to be touched off by accident if you're not minding your trigger finger. A long double action trigger is more safe because of the long, heavy stroke. However, precision shooting is much more difficult unless you're trained in good trigger control. And of course, if you're well-trained then you probably don't need a double action trigger to begin with! Those who despise DA triggers will buy a SA auto. Those who are afraid of SA triggers will buy a DAO (double action only for every shot). And of course many feel only the first shot needs to be protected against an accidental discharge, hence the prevailance of pistols that are DA only for the first shot.
Regarding safeties that prevent the gun from firing when engaged, some folks want one to add an extra measure of safety, or to temporarily foil someone who snatches your gun from you (giving you precious extra seconds to get it back or go for another weapon). Others however feel a safety will get in their way while under stress and don't want one.
Regarding decockers, if your gun is a combination DA/SA you need one to safely return a cocked hammer to the at-rest mode. If the gun is DAO then it doesn't need one, and thus won't have one. A decocker will either work as a safety as well (such as on Beretta 92 pistols), or it will only decock the piece and not prevent use of the trigger (such as on SIG pistols).
Firing pin safeties simply lock the firing pin until the gun is fired. They prevent a dropped gun from going off accidentally. Many older firearms do not have one. And of course there are those who say new guns don't need them either, as they feel that they complicate the design and are failure-prone.
Anyway, folks will argue the various merits of each to no end. In the meantime, smart manufacturers will offer a model in each configuration and hope for the best. I wish I could help you decide which mode is best for you, but in the end it boils down to your skill with a firearm. If you're inexperienced a DA trigger will be safer, but you'll also have a harder time hitting your target. The reverse is true for a SA trigger. Glock invented their so-called "safe action" trigger that supposedly is the best of both worlds (heavier than a SA, but lighter than a DA), but of course there are those who say it is a jack of all trades, master of none. Like I said, it's impossible to please everybody.