chaya sita or real sita ?

As others have said, it depends upon which is your favourite version of Ramayan, and you are free to choose your favourite. But as nneeiill said (bit tricky, typing her username correctly), real or chaya, simply doesn't matter. 

Maybe we could look at it this way. Let's talk about two versions only, Ram Charit Manas & valmiki Ramayan, otherwise this post will be too long. 

Talking of RCM, when from the first page to the last, readers are reminded again & again that Sita & Ram are the Parmatma, and then, readers are also told Raavan was unable to cross Lakshman rekha (and do remember that Tulsidasji has described both Lakshman rekha & Raavan's inability to cross it, in Manas, but not where he should have ideally mentioned it, but way later in Lanka Kand, during one of Mandodari-Raavan conversations), then to say that though Raavan was unable to cross a line drawn by a parikar (Shri Lakshman) of Maa Sita, but moments after that, was able to abduct the Parmeshwari herself!!, you can see for yourself that this makes little sense. But Raavan needed to abduct someone for this play to progress, so he is allowed to abduct an image of Sita.

But this line of thinking which I've just mentioned can easily be negated by any incisive reader of RCM & Valmiki Ramayan, because a keen reader can easily point out that in Valmiki Ramayan (VR) too, from beginning till end, sage Valmiki has established again & again & again that Sita & Ram are the Supreme Being.  

For example, when Valmiki describes what Mandodari says (after Raavan's death I think), he very clearly & unequivocally establishes the identity of Sita & Ram as Lakshmi & Vishnu respectively. Read those verses where Mandodari says, "Ram is the supreme yogi, the eternal supreme soul without a beginning or an end. Ram wields a conch, a disc, has Srivats (Lakshmi's mark) on his heart, unconquerable, perpetual, the never changing supreme soul of creation."

Further, Valmiki then establishes the identity of Sita by saying, "Sita is the earth of earth, Shri of Shri (lakshmi of lakshmi)", and so on. He also establishes that Sita & Ram are one, and not two, by describing both of them using same words, "Shri of Shri."

Rama is the illuminator of Sun, the God of fire, glory of glories, God of gods, even Shri of Shri (husband of mahaLakshmi.)- Sumitra-Kaushalya conversation.

Rama is the sheltering tree, the supreme refuge, the supreme protector of all, the only personality who is to be praised. – Tara telling Bali.

Devrishi Narad telling sage Valmiki, "Sita is the eternal consort of Lord Rama, most dear to him, like his own existence." (I remember Valmiki's exact words in Sanskrit, "Ramasya bharya nityam, prana sama hita.")

Sitaji telling Devi Anusuya, "I don't emerge from a mother's womb."

Devtas telling King janak, "Sita is a divine child without a match."

So when Valmiki establishes so many times the identity of Ram & Sita, then why no mention of chaya Sita in Valmiki Ramayan? I can answer this by concentrating on the primary concern of sage Valmiki when writing the Ramayan. Valmiki says right at the beginning of his book that, "Sita's story is the most important aspect of Ramayan ("Sitaya charitam mahatv"). 

Then he narrates the entire story to Lav & Kush. Now, as you said, it's when we don't mention chaya Sita, and when we read about Sitaji's second vanvaas & stay at Valmiki ashram, the story of Sita becomes that much more anguishing, more aching to the heart. Maybe that's what Valmiki wanted, especially when he knew that he will be recounting the story to the sons of Sita.