Welcome!

Yes, you can get a full experience with GC3.  Obviously it won't be the same experience... 

There is a game timeline in the Campaigns screen. 

In general, what happened in the earlier game(s) happened earlier in the galaxy than GC3.  But the games are more iterations of the same concept than consecutive stories.  SD redevelops the internals and takes the occasions to re-do the universe and game design.  (I put that badly.)  Just know that they aren't intentional sequels.

None.  The recent DLC is just adding some Star Control characters and races to the GC context.  Could be some fun alternative races; the old ones do get stale after a while.

Don't worry about it.  There's so much to do before you ever see one, if you do.

Easy to do in GC3.  Just don't select Drenghi as a opponent.  This game isn't locked into a story, except for the Tutorial campaign.  The AIs are strong enough (especially at higher settings) to act quite independent of a story.  And, of course, custom races are pretty easy to do, even without mods.  But play for a while before you head off in that direction.

So with the Gold Bundle, you have all the expansions (I don't).  What are you planning to install?

If you're on Steam, you might want to start with the 3.7 version without Mercenaries or Intrigue.  They complicate things.

You don't really need to understand any backstory.  Just the civilization traits, and what each trait unlocks in the tech tree.  Knowing who the Drengin are is unimportant, but knowing what Slavers can do for your planet IS important.  Gameplay will fix that.  There's really nothing much to read up on (other than helpful posts).

EDIT:  to reiterate, knowing any story from any previous GalCiv is not at all necessary.  And the other game that they put a crossover DLC out for?  I deactivated that DLC.  I found it annoying.  Don't have the other game, don't want the other game.  Doesn't ruin enjoyment of this game.

By the way.  There is a nice manual that seems to discoverable only by accident.  (The 'Manual' button on the main screen is broken.)  Look in your install directory.

E.g. ..\Steam\steamapps\common\Galactic Civilizations III\  for the file GalCivManual_2018.pdf (or something like that).  It will help much more than the wiki or posts here.

Ok first is the Mithilar a human being that slid over from another universe. In the beginning this universe had no sentient beings. He then took a crystal and made five beings. Three were energy, and two were physical. They are known as the Arnor. 

Then the Iconians  evolved. The two physical Arnor were decided on what to do with the Iconians. One wanted to help them grow. The other wanted to destroy them. 

This caused a civil war. The ones that wanted to destroy the Iconians were the Dread Lord's, while the ones that wanted to help the Iconians were the Precursors. Appearently by this time the Drath evolved on Altaria. They are a reptilian species. There are no primates on this planet. The Dread Lord's created a species called the Altarians to serve them on the planet Altaria. The Precursors helped the Drath to escape the planet Altaria.

The Your were created by the Iconians to serve the Precursors. Eventually the Precursors trapped the Dread Lord's in a pocket universe, but not before they made the Yor sentient, and created the Snathi. The sentient Yor turned on the Iconians almost wiping them out. The Precursors disappeared.

Later on other species evolved, including the Drengin, and the Arceans. The learned the Stargate, and made war with each other. The Drengin flew there ships 10,000 years, and conquered the Tori.ans. through gorilla tactics the Torians made it not feasible for the Drengin to rule Toria, and got their independence.

The Arceans meet the Humans, where the humans take the Stargate technology, and combine it with fusion creating the hyperdrive. Beating the Jessiuns by 6 months. The Drengin steal the hyperdrive technology. To fix this the humans give the house perdrive to everyone. In the mean time the Drengin pinn the destruction of the zandar on the humans. The Thalans slide in from another universe at a later date where the hell man's destroy the universe at a later date.

Now comes the galactic war. At least who they knew were in the Galaxy at the time. One side led by the humans. Was Humans, Arceans, Torians, and Altarians against the Drengin, Yor, Drath, and Thalans. While this is happening the Drengin experience another civil war where with the help of the Yor they defeat the Korath, and the Dread Lord's who escape their pocket dimension. Only to win the galactic civil war taking.everyone except earth. Eating Torians.

Now there is another war in three.