I've got twins already (girls, nearly 4 now)....good luck
You'll need something with lots of space & storage - ie, boot big enough to get double pushchair in and out of easily, that's easy to lift the car seats & babies in and out of aswell (you'll be doing it hundreds of times so little things like this become important).
We also found that having a vehicle where the seats are high enough for the kids to get a good view outside on a long journey can be a real stress-saver. Tables in the back that they can put their toys, kiddy walkmans and drinks on have been a bonus too.
Not sure what you're budget is - mines not vast, so the Renault Scenic did it for us - doesn't set the World on fire to drive, of course (but I've got to like the slightly higher than normal view ahead), but is comfortable and has a lot of equipment for the money (standard Aircon, ABS, 4 airbags, drinks cooler! etc).
A good spec one (with the pokey 140bhp 2.016v) can be had new for about £14-15k I believe.
Like the look of the 307SW aswell, not so sure about the Picasso (but even better value than the Scenic). Zafira and Avensis Verso may also be worth considering.
New Scenic coming to the UK next year - think we can expect something quite radical if the new Megane, Espace & Vel Satis are anything to go by.
Hope it helps.