The environment for adventuring will be built around humans and demi-humans for the most part. Similarly, the majority of participants in the campaign will be human. So unless the player desires a character which will lurk alone somewhere and be hunted by adventurers, there are only a few options open to him or her. A gold dragon can assume human shape, so this is a common choice for monster characters. If alignment is stressed, this might discourage the would-be gold dragon. If it is also pointed out that he or she must begin at the lowest possible value, and only time and the accumulation and retention of wealth will allow any increase in level (age), the idea should be poperly squelched. [Note: Gygax nowhere suggests, here or in any of his other D&D material, giving class levels to monsters. The starting PC will be a very young gold dragon, and will advance per the dragon aging guidelines in the MM. Nor will this character 'rampage across the campaign for awhile, as he will be massively more powerful than any of the other characters'. Its power level will be mostly static (over the typical time-frame of a campaign), while it won't take too long for the rest of the group to heavily overpower a very young dragon. And I don't see any mention of titans anywhere in this section.) ...
As to other sorts of monsters as player characters, you as the DM must decide inlight of your aims and the style of your campaign. The considered opinion of this writer is that such characters are not beneficial to the game and should be excluded. Note that exclusion is best handled by restriction and not by refusal. Enumeration of the limits and drawbacks which are attendant upon the monster character will always be sufficient to steer the intelligent player away from the monster approach, for in most cases it was only thought of as a likely manner of game domination. The truly experimental-type player might be allowed to play such a monster character for a time so as to satisfy curiosity, and it can then be moved to non-player status and still be an interesting part of the campaign ...
So you are virtually on your own with regard to monsters as player characters. You have advice as to why they are not featured, why no details of monster character clases are given herein. The rest is up to you, for when all is said and done, it is your world, and your players must live in it with their characters. Be good to yourself as well as them [note: what a radical concept!], and everyone concerned will benefit from a well-conceived, well-ordered, fairly-judged campaign built upon the best of imaginative and creative thinking.