If you join one at character creation it’s free, otherwise you need to get Arcane Mark cast on you, this will probably cost you a mana crystal and change :).
Benefits wise, if you want to get involved in Conclave it’s pretty necessary even aside from the ability to speak you really need a group of people to gossip and scheme with.
Orders can also be a vector for some types of plot, The Shuttered Lantern I know had some spy stuff going on as they’re intelligence and counter intelligence types. I also know that some Eternals and heralds are going to want to talk to specific kinds of mage, Autumn Heralds interested in trade would go looking for Golden Pyramid mages.
Also the Grandmaster of an order gets Mana and a small amount of materials each game and if you can convince them to support you, some of that can be yours. Obviously being a member of their order in good standing can help there, but also simply having a convincing and well thought out plan can work on Grandmasters not your own.
How organised the orders are really depends on who’s Grandmaster, Shuttered Lantern in my experience was quite organised, I don’t know about the other orders.
Personally I’ve had good experiences and even when an order was a bit disorganised I saw it as an opportunity to make something good of it. So I would recommend, it’s a good way of meeting likeminded people if nothing else.