When wiring up normal 3-prong outlets, does it matter if I
switch the black and white wires on a single outlet in the run?

Please, hire an electrician.

OP doesn't necessarily have to hire an electrician, but does need
more knowledge before attempting to DIY this job
Electricians aren't born with their knowledge. They have to learn
it. There's no reason a person of ordinary intelligence cannot
learn, in a reasonable length of time, how to safely perform
simple, basic tasks like wiring an outlet, switch, or light
fixture.

In short, yes it matters, and you have to know why. Home Depot and
Loew's sell good books on home wiring.