Liaoning is a good choice because it's labeled as a trainer.
Sending Liaoning to PACRIM will come in due time, maybe after Shandong is commissioned. Still 055 is too new for such kind of a thing, it's not typical Chinese.
Sending Liaoning to Indian ocean will take longer, maybe after 002 is commissioned.
In the foreseeable future China is not interested in global power projection. It would rather be a two ocean Navy. Though that doesn't mean Chinese ships will never sail in Atlantic, they already do. But showing off two carriers is too excessive unless you really want to be a global Navy. That would be a message to US Navy saying ”I want to be like you”. In certain aspects, yes. In many other aspects, no.
Maybe not 2 but if I'm in charge I would certainly send at least Liaoning on a global goodwill cruise. Certainly visit most of the major ports in Asia, Australia and PACRIM including Pearl.
Then follow not long after to the Indian Ocean including India, Pakistan, Mideast and the Med. If planned properly, they could certainly pull that off in 2019. By that time a proper CSG including all the air wing would've been firmly established.
It would be a good 'coming out' party for PLAN as they transitioned from green water to a true blue water navy