Foil
Foil teaches patience. Right of way means you can't just attack — you have to earn the touch. The discipline you build in foil is the foundation that transfers to sabre and épée.
A weapon you have to earn.
Right of way is the rule that defines foil. If both fencers hit each other, only the one who attacked first — or who parried first — scores. It's the rule that makes foil cerebral, and the rule that makes foilists the best technicians in the sport.
Equipment
Foil is where the modern sport began. The blade is light, the target is the torso, and the rules — right of way — exist to keep the fencing intentional. You can't bull-rush your opponent. You have to set up the touch.
What that means for a beginner: foil is the most discipline-forward weapon. Early lessons are about footwork, distance, and reading the other fencer — exactly the foundation that transfers to sabre and épée later. Most US fencing programs start kids on foil for this reason.
If patience and tactics appeal to you more than speed, foil is your entry point.