It is always correct to split two full sentences with a period (full stop). But, you may use a semi-colon or colon to join separate sentences.
But, where to use each is largely determined by the intention of joining those sentences.
If the sentences are merely related, then a semi-colon is a good choice.
Mary ate dinner; she had roasted chicken.
When the second sentence is really the thrust of the first question, a colon makes for a better choice. (In other words, it explains the first sentence.)
Mary ate dinner: it was roasted chicken.
In your particular example I would choose either the period or the colon based upon the above reasons.
Addressing your capitalization choices. The only punctuation mark of the three that requires capitalization after it is the period (full stop).