Probably all of the above.
I've never played any campaigns so that's not necessary but I would think that they would be helpful. Certainly the "getting started" document and the manual are required reading. I did do the tutorials and found them to be very helpful. Also I did a web search for "GalCiv2 faq" and found a very nice "must read" FAQ/Strategy Guide by cyberj914. It can be found at
here at Gamespot by clicking on the FAQ tab.
There are two guides listed, the one by cyberj914 is very old (written for v1.1 of Dread Lords) but even so I highly recommend that you read it. There's another that's a little more recent there by mi64 that I haven't read so can't vouch for.
As far as Dread Lords (DL) or Dark Avatar (DA) the above specifically apply to DL but I recommend it even if you decide to skip DL and go right to DA.
As far as that point it probably is more direct to just play DA as that is the current version and you don't need to have played DL to play DA.
Finally use these forums as a source of information both by searching for old threads where there are many gems of wisdom as well as simply asking direct questions.
However with all of the above said it will take many games for you to get used to the game and refine your style. I started by reading the above and just playing but I would guess that I didn't bother to finish the first ten games that I started. I'd get halfway into the game and have already learned a bunch of stuff that made how I started the game obsolete so I simply started a new game using what I had discovered but usually at a higher difficulty level.
Certainly don't be afraid to use the difficulty levels but I recommend that you don't linger too long on the lower levels since they can allow you to develop bad habits. Cakewalk AI pretty much just drool and is only really good for learning how to move ships and build planets and basic game mechanics.
I think once you hit Normal the AI start to be more aggressive and from there on up can be a serious challenge. The first time you hit that level it can be a shock. You think you were doing a good job colonizing and building up planets but you'll find out that you really weren't.
Anyway, this is not a game you're going to pick up and excel at in a week, but it's well worth the effort it takes getting into the game and the better you get at it the more you'll enjoy it.