After you have the internet connection, why to you need esoteric stuff like a raspberry pi?
also, on the topic of internet connection, at least the contracts i've seen (AT&T, Verizon) you can't have any 'server' or accept any connection initiated from the outside in your home account. As crazy as it may seems, this is on the contract you probably signed to have internet.
The point of bringing in the RPi was to create a node that is always-on, because there is no central file server when using BTSync. RPi makes sense because it's cheap and low power, but just use your imagination. I really doubt it was intended to be esoteric. Instead you could use an extra computer you already own that can stay on 24/7, or a VPS.
also, on the topic of internet connection, at least the contracts i've seen (AT&T, Verizon) you can't have any 'server' or accept any connection initiated from the outside in your home account. As crazy as it may seems, this is on the contract you probably signed to have internet.