What @macfranc says, or if you rent a managed mastodon server here for instance I would estimate(I am not a Mastodon admin) at least around 10-20€+tax,
but maybe you might not need to host your own Fediverse(Mastodon/Frendica/…) server(except maybe for the already existing PeerTube Server).
Firstly
if budget would be a problem, as well as additional manpower for administrating, it might be a good idea to stick to one of the already exiting instances and create an account there.
There are already quite a lot Pirate affiliated servers out there, see this list in the German Wiki.
Secondly just spinning up a - lets say Mastodon - account, would be much quicker in any case, and than you or the PR ppl can probably better see the limitations etc, and even if you later on decide to host your own Mastodon server, account migration between Mastodon instances is very easy, all followers can be transferred to the new account.
Thirdly due to the federated architecture of the Fediverse, creating an account on a public server can give - at least initially - better discover ability than creating one on a private server, since Mastodon users dont really see posts of accounts they dont follow unless they are on the same instance(or a user they follow shares the post).
(Of course issue Nr. 3 is mostly irrelevant once the account has reached a certain size, or a few posts are widely shared across the network. However as I mentioned secondly, migrating an account from one mastodon server to another is very easy, so you could just migrate once you spun up your own instance)
Frendica or other Fediverse platforms
Of course Frendica accounts could also be migrated, however AFAIK the feature is still experimental, so it might not work as well. Also Frendica is more Facebook like, while Mastodon is more Twitter like from an interface and interaction point of view.
Pixelfed would be the Instagram like alternative, while users of all of these services can follow and interact with each other, depending on the users platform interactions can be limited. Which is why I recommend using a platform that fits the desired use case best. I.e. probably Mastodon or Frendica in your case, for a general purpose Social Media account.
PeerTube
While I said that you dont really need to host your own Mastodon/Frendica server just yet, for the reasons listed above.
A PeerTube(basically the Fedivers’ YouTube equivalent) server might still be worth hosting yourself, since 1. you already have one(update it please)^^, 2. storage is still a bit expensive so uploading a lot of videos would probably be a big burden to most public PeerTube instances, 3. If we embed the PeerTube videos somewhere it might be a good idea to have them “internally” so that we wouldnt involve a third party, and 4. again we already have one and there would even be potentially fresh demand to use that server (for instance by the psc, as mentioned in my other thread)