M.K.
Hi Jenn -- Welcome to the "2 under 2" club!
Without a doubt, you will definitely need a double stroller!! Heck, I STILL use mine (even though my daughter is almost 3) because it better ensures the safety of both kids at the same time. Being able to strap down your toddler will become a necessity at certain times. And there was no way my daughter could have handled a sit-and-stand at 15 or 18 months. She would have jumped-off and made a run for it!
The previous poster made an excellent point -- you will need help. I did not have any family in the area and I ended-up hiring a part time nanny until my baby was about 7 months old. This allowed me one-on-one time with both children, which was especially important for my first born. Even someone as young as a preteen to serve as a Mother's Helper a day or two a week will allow you to get a couple things done at home.
I highly recommend buying some outdoor play equipment (climbers, playhouses, etc.) and toys (chalk, balls, etc.) so that you and your first-born can get out to the backyard to play during all the baby's other naps. I found some great used outdoor playsets on Craigslist. If you are strict about naps/sleep being in the home (vs. on the run), playing outside in the yard or on the driveway will be a lifesaver for you.
Finally, I strongly recommend keeping any major transitions for your firstborn either 3 months before the baby arrives or 3 month after. I don't know if you need to change rooms, but this is a pretty big transition for a little one -- even without a baby coming into the house!
Oh, and take time to wean your child from any equipment that the baby will need, long before the baby arrives. For instance, consider transitioning your child to a booster seat now and putting the high chair away. Your child will forget about it and won't feel that the baby "took it" away from her. Same with all of the infant/baby toys. Time to put them away so that she forgets about them by the time you pull them out for the baby.
Sorry this is so long! Feel free to contact me if you even have any questions!! And congratulations again!