Foil is the most common starter weapon. It is an excellent weapon to begin with if you have no preferences or want to learn generalized principles of sword fighting. Transitions to the other weapons from foil are relatively straight forward. Foil is an abstracted form of fencing that emphasizes proper defense, and cleanly executed killing attacks. Historically it was a training weapon for the small sword, so it is well suited for the purposes of learning. However, it is far from a simple weapon, and many experienced fencers return to foil after trying the others.
Sabre can sometimes be an effective starter weapon, for a few reasons. Like foil, it has rules of right-of-way to emphasize proper defense, and its de-emphasis of point attacks can be a relief to a beginner who doesn’t yet have much point control. Also, in some areas it may still be possible to compete in dry sabre competitions, meaning that it can be the cheapest of all weapons to compete in (although electric sabre is definitely the most expensive weapon). However, sabre differs from foil and epee in a few key respects that can reduce its effectiveness as a starter weapon if the fencer plans to try the others in the future. Among these differences are the aforementioned de-emphasis of point attacks, and a different sense of timing and distance.
Epee is sometimes used as a starter weapon for two reasons. First, the rules are simple and easy to grasp, and second, the equipment costs are lower, since no lamé is required. However, the apparent simplicity of the sport can obscure its subtleties to the beginner, and make progress difficult later on. Furthermore, the lack of right-of-way in epeé can make transitions to the other two weapons difficult, if put off for too long.