You use "ce" you provide a certain opposition to what has been said when that is not what matters much (for instance, someone’s is trying to guess what your problem is what they say is not the description of your problem); however, if there no such context you can still use "ce" and there is no great difference between the two; you can then omit it.

(ref)
Le problème pour moi est que je dois me trouver devant mon ordinateur à midi et à 18 h 30. Je suis comme une chèvre à son piquet.

Both sentences are correct and idiomatic. I would say the difference between them is at most a slight nuance, as using "c’est que" you actually repeat twice the subject (the c being "the problem"), thus insisting even more on it, in this case on the fact it is a problem.
If the sentence is long enough you could use this also in order to bring back the subject "closer" to the verb:

Le problème, pour peu que ce soit un problème car l’offre de transports en commun est assez étendue et quoi qu’il en soit nos enfants peuvent se déplacer à vélo, c’est que notre nouveau quartier est assez loin du collège.