It depends on the format you want to create the website or webpage.
--I think if your page is going to be text-only, you could make a webforum on Ezboard,
or a derivative of Ezboard if it's no longer available.
--A webpage w/ images would be require a more significant amount of attention,
from the host server administrators, and I would recommend doing a search on
Altavista to get current results for a webhost.
--A website to host video on a fansite for free is extremely uncommon...
AFAIK (As far as I know,)
I can't make any legit recommendation for posting videos on the internet.
I just wouldn't recommend posting videos on the internet. It requires too much
attention from server host administrators to verify
that they'll be able to display the video indefinitely.
--"Completely free" on the internet means basically use Internet Relay Chat (IRC).
I'm absolutely certain you could find an IRC server and channel to talk there.
The price of getting a server to host the page is proportional to the amount of
attention it takes the administrators
to verify what audience the content is appropriate for.
- Text = "free"
- Image = free w/ advertisements
- Video = pricy, at the very least, the host will profiteer off of a video upload
- Internet Relay Chat (IRC) = text-based chat, others are allowed to respond in kind
Lastly, if your fanpage is meant to host Trek-inspired music or ST song covers,
I'd highly recommend changing it to a professional format instead'a a fansite.