A short introduction to the evolution of Mayan languages is in Inga Calvin's hieroglyphic decipherment guide, which is available online at the FAMSI website.

The dominant dialect of Mayan spoken during the Classic Period is known as Ch'olan. An ancestral version of Yucatec Mayan was spoken in the North, and a dialect ancestral to modern K'iche and Mamean was likely present to some extent in the southern Highlands. There may have been other dialects, but scholars appear to have some disagreement on the topic with different scholars proposing different evolutionary trees for Mayan languages (discussed by Calvin in the source above.) Nevertheless, the majority of Classic Period inscriptions appear to conform to the same Ch'olan dialect.

During the Postclassic, after the fall of most of the cities in the Southern Lowlands, the Mayan languages split into a couple dozen dialects, with Yucatec Mayan becoming the most common. During the Colonial period, as Spanish becomes the lingua franca and indigenous groups become more isolated form each other, this process continues producing the tangled mess of dialects that characterize Mayan languages today.

As to which dialect most closely resemble the Classic Period Ch'olan dialect, that's tough to say. There are several dialects believed to be directly descended from Ch'olan, including Chortí, Choltí, Chontal, and Chol. Although none of them are really faithful representations of the original Ch'olan any more than modern Italian resembles classical Latin.

Hi there.

While you might get an answer here, you might also consider asking over at /r/AskAnthropology or /r/AskLinguistics, especially for your follow-up question.