Omega is the prequel. Then 1, then 2. But it doesn't matter, as the plots are independent. (That's what they said to me when I did the same question. Then I've been playing only the 2nd game and I've had no problems at all.)
Actually, CR1 and Omega are closely related -- CR2 not so much. I would play CR1 and Omega in the order they were released. BTW, make sure to replay CR1 with all the character sets, and go back to previous characters since new endings pop up after you complete multiple playthroughs. All in all I took me about 25 hours to finish the whole game (including the final boss fight). Easily one my favorite RPGs of the last few years on any platform.
I agree with squarezero. Entirely finish chaos rings. Then move on to omega. It's the order they were released in. There are a lot of twists in the story and it seems like they were meant to be revealed in that order.
I didn't know Omega was closely related to CR1, someone told me quite the opposite. -__- Anyway, as a player of CR2 I can assure that the references are all understandable for newcomers. Actually CR2 is the last release, I got it a few days after launch. So it's CR1, Omega, CR2 (as stated by squarezero), but Omega being the prequel.
I didn't mention chaos rings 2 at all. I finished chaos rings. Then moved onto omega. Haven't finished omega completely yet though. So I hadn't moved on to 2. From what I understand 2 isn't so closely linked as 1 and omega and could be played as a stand alone game without missing too much.
Chaos rings omega has probably the best storyline of the 3 but you will need to have finished the first chaos rings to fully appreciate it. The original chaos rings can be repetitive since you have to play through all 4 couples to make it to the true ending while the areas and the monsters don't change. I personally didnt find this to be much of a problem since I found the semi complex storyline to be quite interesting and im used to grinding in other games. Still each couple has their own story and there are some good plot twists. I would recommend playing Escher and Musiea first, then Ayuta and Mana then the other two couples in any order. Oh and also try not to grind if you don't want boss battles to be really easy. Chaos rings 2 is almost completely unrelated to the first two games, although the story still takes place in the same verse. CR2 is considerably superior in every aspect compared to the first two games except maybe story but that's down to personal tastes. If you intend to play CR1 and Omega then play CR1 first. CR2's storyline is unrelated to the first two games.