The easy part is to have it download into a directory which is the date the picture was taken. ZoomBrowser (which you already listed) can do that, and I bet others can too.
It sounds like you want to number the pictures based on the sequence in the directory and not what the camera produced. So you want to rename the pictures as you copy them. This I'm not so sure about. I've never heard it listed as a feature before, but I'm certainly no expert.
I haven't used it, but I know many, many people who like the software from breeze systems called... Downloader Pro. Their other product (breeze browser) is very well respected. You can find out more about it from here:
I can't specifically say that it does what you want, but it's worth looking at to see if it does.