Is there a reason you can’t simply modify the timestamps to force-order them?
Otherwise, plugins like my CG-PostOrder plugin (which needs to really be revised for WP2.x), Adhesive, etc. might meet some of your needs. PostOrder was specifically designed to allow a numerical ‘rank’ to each post, so you could force order them.
BUT, you could just as easily do things like timestamp mods, sort by name and alpha-sort (start with numbers…), or use a custom post field with the sort number and sort on that (which is basically what PostOrder does…).
But just your description above really doesn’t define how, say over the course of a year, you’ll want this stuff to work. How many posts will you have total, how many do you want to ‘sort’, do you want them just ‘sorted’ on the homepage or in index pages too, etc.?
The idea of posts is entries that are in a chronological order. If you want to change the order change the date. But if the date is of no importance then you should just use Pages – there are several plugins for sorting Pages.