Current month as ‘home’ page

I asked this before, perhaps 6 months ago or so, and got some tips but I still can’t figure it out. I haven’t thought about it much since, but recently I stumbled into it again:

At this moment WordPress starts with showing ‘x number of posts on the startpage. What I would like is to show all the posts of the current month that actually has posts as the startpage. This was the way it worked with Movable Type untill I switched to WP more than a year ago. But I still miss it.

What I don’t like about the setup as it is now is this: When you visit the homepage you may see 5 most recent posts if I set that number to 5. Perhaps these 5 posts are all from the month of july. The visitor has now two choices: He chooses the month “july” from the dropdown list and perhaps gets to see only those same 5 posts if that’s the total amount of posts in that month, or he chooses “june” right away or one of the categories.

Therefore I find it more logical and more clear to the visitor if the homepage would start with the current month (IF it has posts, otherwise the most recent month WITH posts), and also show the monthly navigation right away (I’m using the one from ScriptyGoddess).

Any tips on this?