You don't -need- to play the rest of the series first, but if your main interest is the campaign the general consensus is that DoW2 and CR had a better one. The campaign goes for a lot longer, the levelling and gear is more in-depth, and the story line is more interesting. The drawback of them is you only have the one race, Space Marines. But it's still much better overall IMO.
No, Chaos Rising's campaign still has you as the Blood Ravens. It's a continuation of the story from the original. Personally, I preferred the original campaign to the one in CR. Mainly because they had infinite missions, and gave you a chance to earn more levels and wargear. CR's campaign was short and very linear.
How many different campaigns in this one?
One. You just get to do it as all 6 races. But the missions and levels and general story is the same for everyone. They're also very short, with no real options. And you won't get nearly as much wargear as in the last two campaigns.
If you are going to get into DoW2 at all you should really do yourself a favor and start with the original DoW 2, then Chaos Rising, lastly Retribution. Main reason behind this is a lot of stuff in CR or Retribution is not going to make sense to you because the games are following a one extended storyline.
Also you should keep in mind that while Retribution's campaign is indeed shorter and its level cap is lower(10 compared to original's 20), it is still 6 different races that you get to play as and level up, customize their stats and collect different kinds of unique wargear for. That equates to a lot of variety.
Anyways hope this helps. Also did you play the original DoW series? Because if story is really your main driving point, you should really start with the original DoW.
Hope is the first step on the long road to disappointment
The problem with this one's campaign is that while there are 6 campaigns, they are almost exactly the same. In Retribution you can play as any of the races, but as I said earlier, the campaigns really just copy and paste from one to the next.
Now, the campaigns are 16 levels each. Again, the levels are almost identical race to race, you're just using a different race to play as and may face a different enemy on a map that has the exact same terrain race to race and the exact same objectives. Most people I've seen post get bored of doing the same campaign with a different race, but some people enjoy it. Granted, I've not heard anyone say they enjoyed it 6 times.
You also said you like skirmish. If you liked skirmish in the first game... You may not like this one. The scale and gameplay is entirely different. You'll need to watch some replays. Also, the AI is really not very good. Again, watch some replays.
Honestly, I'd stick to the first DoW series for you. The campaign in Retribution is no where near as good as DoW2 and CR, and it follows DoW2 and CR's campaign storyline, so to really get what's going on you need to play those first(especially Chaos Rising).