The Speedy 30. I know it's an LV classic, but I'm not a handheld bag kind of girl at all. At least the Speedy B would've came with a strap option, but then I wouldn't have been satisfied with the floppy bottom. Sigh. I can't decide to sell it or pass it on later, especially when I bought it for such a low price years ago.
Maybe try a base shaper? I use them in all bags and it makes a world of difference. I buy a size smaller so the edges don't wear on the bag.