Well, after reading some additional on-line game reviews, plus watching several Youtube videos by DasTactic, I finally decided to play using only the base game plus the Crusade DLC for my post-Tutorial games.

Got part-way through my first regular game, and was having lots of fun cranking out explorer ships to use for snagging artifacts for bonus money.  However, the other civilizations were too often beating me to the best planets for colonization.

After watching DasTactic's videos, I now understand the critical importance of cranking out Colony ships early and rushing to grab the best nearby planets, before trying to snag all those artifacts and space junk items.  Therefore, I plan to start a new game later today, and will try this new rush colonization strategy (still using just the Crusade DLC).

I have played just Crusade quite a bit. Its enough of a game to be entertaining. Not the greatest game, but it works. I'm only just starting to warm up to the various DLC.

Don't play the base game without Crusade. The base game is different enough that you will need to relearn how to play. Nearly all the DLC is built for Crusade.

I like the DLC that adds new civs to the game, such as heroes and villains of Star Control. I have activated nearly all of those DLC without a second thought.

Mercs might be difficult until you learn how to deal with powerful fleets. Some merc ships might be as powerful as a dozen regular ships combined. They might have moderate to high weapons and defenses in all types, and maybe have some ability to dodge 75% of all damage. Or something like that. The point is some mercs are a one-ship-fleet.

Intrigue has governments. I did not like. The governments makes it difficult to have a large empire, or to do the things you can do in Crusade such as the ability to use shipyards to fund missions. I don't remember much about as I haven't play it in a while.

Retribution adds new content and rebalances the game. You can build supply ships to provide construction points to planets, you can make space lanes where ships can move faster when traveling along the lanes, and planets get some special artifacts that give you powers to do stuff (including damaging enemy fleets from afar or making dead worlds habitable).

I recently played 2 games with the Intrigue DLC installed. I did not like. When I had more planets than what my government would allow, I kept getting notified every turn that I should change things. I did not see anything I could do to turn it off.

Some governments only work for certain ideologies. It does not say this in the tech tree, so if you see a government you like, be certain to double the government window to check what it requires before getting your hopes up.

When you create a commonwealth, you can't make any changes to them after you create them. You can't remove planets from them and have them join your empire. You can't give them more planets. I found that while they start out with your tech, their tech develops independently of your own. I even had an enemy empire surrender to one of my commonwealths. I found that they can build trade ships and constructors. This suggests that they might compete with you for resources.

I did like the galactic market. You can buy resources for about 1000 credits, and sell them for about 200 credits. They had galactic resources all in one place. You don't have to shop around with other civilizations for what you need. You don't have to wait x turns before you can make another deal with them. Though, you seem to need to wait for a civilization to sell some resource to the market before you can buy it, so it might be difficult to get a resource early in a game.

Lost treasures is a way to build powerful ships.

I think Builders and Mech Parts Kit are a no-brainer as it's cosmetic rather than gameplay changing.  Crusader is next, then Lost Treasures, Precursors, and Mercenaries.  The others are more what you want to taste.  The Star Control races might have balance issues (as one of them is dependent on the Commonwealth option for dealing with a growth problem) if Intrigue is not enabled.  I also really recommend that you look up the Workshop DLC races.  They do spice up the predictable matters.

I find Intrigue's Commonwealth system difficult to deal with (in a good way) as you do need to spin off worlds every so often, but you don't get them back without pain.  I think that Intrigue is the most difficult of the expansions for gameplay.  Mega Events are GalCiv3's version of SimCity Disasters, and while they are fun to play, they are intentionally meant to disrupt order and might not be as fun for earlier games.