As for double strollers, you'll probably need a tandem to start with. Unfortunately with those, they can be hard to steer, especially with the heavier child in the front. I had the Jeep tandem stroller and I do not suggest it. Heavy, bulky, really really difficult to steer- more so than other friends' double strollers!
Once your newest can sit up, I would suggest a side-by-side stroller... those turn on a dime but JUST fits through doors. I currently have the Jeep side-by-side stroller and LOVE it! Although it doesn't have a basket on the bottom... and I'm finding that my 2 YO would rather walk than ride.
Another suggestion may be the sit and stand stroller... depending on how much your first child needs to be strapped down! You'll be able to put the infant car carrier in it while the baby is little and then the baby can sit up when when ready. The older child can sit behind the younger... and it's not wide like the side-by-side.