According to Julie Andrews in The Sound of Music, the very beginning is a very good place to start. That may be true with musicals, but it’s not necessarily true with merit badges.
While the requirements for every badge are numbered, there’s no rule that says Scouts and counselors have to go in order. In fact, it often make sense to approach the requirements out of order. (Among the few exceptions is Scuba Diving, where requirement 2 says, “Before completing requirements 3 through 6, earn the Swimming merit badge.”)
Timing will often determine sequence. For example, requirement 8 of Communication merit badge has the Scout plan a court of honor, campfire program, or interfaith worship service. If a court of honor is looming on the schedule, it make sense to have a Scout who needs the badge plan it, even if he hasn’t completed requirements 1 through 7.
As a merit badge counselor, you can also sequence the requirements to pique a Scout’s interest. For example, requirement 7 of Backpacking merit badge (“Tell how to properly prepare for and deal with inclement weather.”) will be a lot more meaningful to a Scout after he has completed a trek (requirement 11) with less-than-ideal rain gear. (You obviously wouldn’t let a Scout venture out totally unprepared, but you get the point.)
When a Scouter complained that one of Lord Baden-Powell’s ideas was against Scouting’s rules, B-P exploded. “Damn the rules!” he said. “Call it an experiment!” In terms of merit badge requirements, think “Damn the order! Call it an experience!” When you do, your Scouts will gain more than just a simple piece of cloth.
For more on merit badge prerequisites–and the lack thereof–see section 18.104.22.168 of the Guide to Advancement.