If this is your first visit to the Magic Kingdom at WDW, I personally recommend driving to the park and taking the ferry or monorail to the MK. This is because Disney is all about the pre-show, and the pre-preshow is the excitement of crossing the lagoon. It is great and the way it was done for decades, so you'll get the full picture.
Besides, you will need to fold the stroller and drag it on the bus, which can be a hassle. The ferry is the equivalent of a roll-on roll-off car carrier (much smaller, though
). You enter via a wide ramp on one side and exit via a ramp on the other. Literally a straight line, with a pause in the middle while the boat sails. The monorail and ferry take the same amount of time to cross, so you aren't loosing time either way. You'll need to roll the stroller onto the monorail car, but it will likely take up a majority of the center area (if you don't need to fold it).
Resort monorails are slower than the express train from the TTC, as the resort monorails stop at the resorts, which takes time.
Finally, if you drive, everyone will have a seat on the way home. After treking about all morning, it is nice to simply sit in the car seat and let the muscles relax for a bit, even if you are the driver it has an effect. Definitely a positive, especially if the little ones are sleeping.
Good luck and have fun!