If you would rather settle into one character than keep several alts moving, Legacy does not require an alt army.
Shared points, separate choices
Blizzard’s Legacy overview says points are shared across your Battle.net account’s non-Hardcore characters. Each character allocates its own perks.
At launch, each character can spend up to 16 points. That is a spending cap, not the total number you can earn. Blizzard says a single character can earn enough to reach it.
When does Legacy unlock?
Most players will earn their first point at level 25. The overview also lists reaching skill 150 in a non-gathering primary profession or exploring the entire world map as alternative first-point milestones.
Gathering professions are not included in that profession milestone. A gatherer can still earn points through other challenge categories.
What should I plan around?
When you unlock the system, read the perks for that character and choose what suits your plans. This is a starting explanation, rather than a fastest-points route or a recommended build.
Choose a character you want to keep playing. There is no need to make another solely because you think Legacy demands it.