When does Ol' Rickety get a shot?

Being an expectant parent brings with it countless new things to worry about, from whether you're capable of handling gut-wrenching parenting decisions to whether there will be enough cash on hand to buy bottles and baby powder. Nothing new or profound there.
But I've got a more practical concern. Essentially, it's this: When the time comes to leave the hospital with the newborn, and then in the ensuing months, I'll have no clue how to actually transport said newborn when I'm out.
Do you carry the car seat? Do you just carry the baby? How about a stroller? What about one of those new-age swaddled baby slings? Why not just put the baby in a grocery store basket, next to bananas and atop a soft loaf of bread?
I'm sure that'll get figured out soon enough, but for now I'm baffled.
We went to a baby store the other day and looked at strollers. Actually, they might as well be called Offspring Hauling Systems because they act as car seats, baby carriers and strollers, and are far more complicated than I would have imagined. Harness contraptions vary, handles are adjustable and I think some even offer sun shields that automatically tilt to accommodate for the changing angle of the sun at different times of the year.
I started looking at another group of strollers, ones hanging from a bin. But it was brought to my attention that you can't just transport the baby in Ol' Rickety from the day you leave the hospital. Ol' Rickety, you ask? That's one of those basic, compact, old-school, collapsing strollers. The informed call them umbrella strollers. They're the opposite of Offspring Hauling Systems.
Anni laughed when I only half-jokingly asked whether you can save money by just starting with Ol' Rickety and, if the baby's head tips to a side, just prop a stuffed animal next to each ear.
My recent attempts to visualize scenarios I'll find myself in after the baby's born prompted this very practical question: If I take the child with me on a quick trip to, say, Menard's, and I set the car seat/carrier on the ground next to me while paying at the register, will women gasp and wonder how a man can treat his child like a bucket of paint?