Most large fans are intended to be used as weapons and to manipulate the winds. They're a staple of tessen users in my village.

Hand fans are very different. They're both ceremonial and social. There's a language to them to how the user moves them or holds it. Their construction is typically far more ornate, especially in the case of ceremonial fans. Materials are lighter and some may have tassels dangling from the hinge. Neither of which is the case with the large fans used for combat.

As for which to start with, it depends on what you need the fan for. As for makers...I've been making my own for years now. Aside from suppliers of the materials I'm hard pressed to suggest a vendor. Especially one that would be local for you. If you have a female friend she might be able to suggest one such place. If not I can try to help you pick a maker on my next trip to Konoha.