Before you leave home, take the canopy, the napper bar, and all extra accessories such as toys, etc. off of the stroller and pack them in your checked luggage. This will not only make it much easier to put the stroller through the scanner, but will minimize the chances that anything will snag during handling and get broken off. The basket should be completely empty. Hook your diaper bag over the handles so that you can grab it and sling it onto the belt.
If your baby is too small to walk, just skip shoes altogether, otherwise try to have him wear the easiest pr. to take on and off. (If he's big enough to walk, he will be expected to do so.) I can't emphasize this enough: NO OVERALLS! They are cute, all right, but they beep b/c of the metal snaps, buttons and buckles. As for your own shoes, wear loafers so that you can kick them off and slip them on.
Presuming you have an adult travel partner, the best strategy is to take baby out while about 10 back in line, then hand him to your partner. Then you pile the hand luggage except the diaper bag on top of the stroller, and go first, letting several other people get between you and your partner. Put the stuff on the belt, including your shoes (your purse/laptop should be your last item, so that you catch up before it ends up sitting on the belt unattended on the other side), then fold your stripped-down stroller and put it on before you step through, gather up your bags and wait. Letting other people go through after you means that if you have to be patted down or if there is something fishy in the carryon, you should still be clear by the time your partner reaches the scanner. (And Baby won't see the strange people apparently assaulting Mommy.) Then baby will toddle through into your arms if he's big enough, or be carried through by the other adult if not. If the alarm goes off on the other adult, the baby can then be walked back through by you, since you have already proven to be clean. This way, at least one of you will always be available to mind your child while the other deals with baggage or security procedures.