I have seen people who have wine totes that are floppier, so if you like that look, you could go with just a basic batting. Just really make sure it is WELL padded on the piece between the 2 bottles so if they clink together they won't shatter.
That look isn't my personal preference. I like a sturdier wine tote with a more structured look. To achieve that, I'd use 72F Peltex by Pellon. It is flexible, easy to sew through & directionless so you can cut it any which way. Pellon recommends cutting it 3/8" smaller than your fabric for bags. A 1/2" would probably be sufficient, in my humble opinion.
Again, though, this is just my personal preference. I love the look of piping & structure. I like the feel of something that is heavier weight because it gives the illusion of sturdiness, elegance & luxury. Either way, I'm sure your wine tote will be beautiful & much appreciated by the recipient. Hope you post pics when it's finished!