Party Setup

I like to use 1 rogue, 1 warrior and 2 mages. Or 1 rogue, 2 warriors and 1 mage.

I personally really like Iron Bull for banter. Sera and Blackwall are fun too. Solas and Sera have a lot of banter as well. I'm now using Blackwall and Dorian but all they do is bicker. I wanted to see if they become friends if I bring them along more but it doesn't seem like it. And honestly I've had it with Blackwall constantly judging Dorian for judging 'peasants'.

Thank you once again! Which warriors and mages would you all recommend for battle?

I prefer the set ups that have 2 males, 2 females, because I find that it is easier to distinguish who speaks when banter triggers that way. I look for a Tank, and prefer 2 mages, one rogue with the tank. The only character that I found to be too hard to have in the party is Cole. I don't like to use Varrick, because I feel he is only a paler shade of his former glorious self in DA2.

Overall, I am not getting a lot of banter.

The party I am likely to finish (or nearly finish, heh) the game with (currently, level 16, in Winter palace story-wise) I have exactly the same set up as themikefest with the Knight Enchanter main + Cassandra, Dorian and Sera. Dorian is the LI for the Main character. That set-up in my experience does not banter a lot. I have noticed that Sera-Vivienne has a lot to say to one another. So, if I did not adore Dorian, I'd go with Vivienne-Sera.

My abandoned PT (at level 10, after arriving to Skyhold) was DW Rogue who was a female, settled on the party of Blackwall (abandoned LI), Dorian (but I was planning to rotate Vivienne in instead if I were to finish that PT since I prefer 2 females, 2 males normally) and Solas.

The banter is going to be subjective, as everyone has different personal tastes. Dorian + Cole are a constant for me, with switching between Cassandra and Varric. Cole, because of what he does, has great and revealing interaction with everyone, so that's something to consider as well.

You might think that melee heavy sounds bad, but I play a SnS warrior (tank), with Cassandra as SnS damage spec (no tanking skills), along with Cole, and Dorian as the only ranged. It seems to work out just fine.

As for actual combat setup, it does help to state what difficulty level you're playing at. I honestly think any setup could work, depending on how you play and gear the characters. All you say is that you want to improve on what you did wrong, but don't say how you found the combat or what your common setup was the first time you played.

Here is the thing for me. I like for players to play the way THEY want to play, what makes them happy and is fun for THEM, not what some random person on the internet says is best. You could play the way people suggest in this thread, with that party setup, but that doesn't mean you will have fun or enjoy it. With that in mind, I think it would be ideal for you to say what it is you're going for, if you already prefer a certain setup, then we can help you to make it work.

phew, tough questions! Party setup really depends on my PC class and specialisation. As others have said, the 1 W, 1R & 2M setup is fairly reliable but if I play a mage with the knight enchanter spec I will sometimes be more flexible with team setup, sometimes dropping either the rogue or warrior while I tank with the enchanter(enemy dependant)

Companion's for banter and interesting dialogue depends entirely who you like and what missions your on. As others have said, fade, elven and magic related quests are great for solas. Magic and Tevinter related quests are great for Dorian, Iron Bull and Cassandra are the more interesting warriors in my estimation. Blackwall is abit dull in banter unless you have someone he gets along with along for the ride, like sera. I agree with Domi, Varric is abit under utilised in DA:I But is a good laugh with cole, dorian and cassandra.

For the sheer rivalry, sera and solas are hilarious, cassandra and varric for their mutual spats and begrudging respect. Sera, Bull and Blackwall and Dorian have some great group banter, that can make it hard to decide which combo to take. This is especially true is anyone of them is the LI.

I'm kind of a min-maxer and have played multiple times on hardest difficulty with most of the trials enabled.  I also made a little spreadsheet to see which party combo had the most banter in terms of minutes.  (Most two-person combos have around 10 mins of banter, but some are over 10 and some are as low as 7 or so.)

Anyway, in terms of gameplay, inquisitor as a rogue is the best.  That's because you will go assassin specialization for mark of death and can open locked doors in single-player areas.  The spec-based focus spells are not important for the inquisitor since you will just use the rift power anyway.  

Then you want a mage.  Barrier is nice, but it's primarily for dispel, which works against opponents with barrier but also destroys demons instantly as they are spawning from the second wave when you are closing rifts.  I prefer solas because of the clumping/weaking rift mage spells, but any mage will do, really.

Then you want a warrior.  Blackwall is probably a better straight tank, but Cassandra is good enough and she can dispel also, so you have two people dispelling the second waves of rifts.

The fourth slot is pretty optional, even on hardest difficulties.  If you want to do all the zones and hunt all the dragons, then I'd add Sera (dual wield) as my fourth because of thousand cuts which does massive single target damage.  If you just want to blaze through the story, I'd do a second mage.  

In terms of banter, everyone is pretty good, actually.  Cole probably has the best banter in terms of the environment.  I didn't use him my first few playthroughs, but now I can't bear not to bring him along.  I think he adds more to the experience of the game than any other character, so now I have to bring him along even if he doesn't fit into my "most OP party" setup.

In terms of two-person interactions, Ironbull + Sera and Viviene + Sera are pretty hilarious.  Ironbull + Dorian also needs to be done at least once.  Solas + Sera is also excellent.  I find Blackwall, Varric, and Cassandra to be the worst in terms of banter. 

TLDR: Rogue (assassin) inquisitor + Cassandra, Sera (DW), and Solas is the most powerful party on the hardest difficulties + trials, in my opinion.  

And Cole, Ironbull, and Dorian in terms of banter, but they really do all have good interactions with one another and sometimes three-way convos in various combinations.