Middle of the month is where you'll see more diversity in decks and less aggro, you can play around that. I don't know about the skill of players. I guess more hardcore players early in the month, and more casual players late in the month.
I think this is a hard question to quantify, mostly because it depends on the month and what the meta is like. In an expansion month like this one, a lot of people gun for their preferred rank as quickly as possible so they can play around with crazy deck ideas when the expac hits. Though likewise, there are others (usually the F2P crowd etc) who don't have access to the new cards yet and so will use their bog standard aggro decks to rinse through the deck-testers to try and get a cheap and low-skill ride to higher ranks.
In standard months, it can often come down to how the meta is shaping. In a fast, aggro meta, rank climbing is quicker and so the higher skilled players will raise through to D and L ranks quickly. But in amore control era, the games take a lot longer and so progression is slower.
The best thing to do if you want to get to diamond (on a normal non-expansion month), is just play as you normally would, get your wins where you can and use your bonus stars. Don't just stop playing because you worry about facing higher level players - this is a good way to get worse because you are denying yourself the practice against higher skilled opponents.