You will not find any free hosting that has the type of support that you need for your own forum(ie: FTP, PHP, & MySQL). They simply do not exsist, for the exception of something like a 5mb storage, which is far too small for what you need.
I know there are places that will host a board like this, like invisionfree.com, or something like that.
But you have very limited options on the board and it has a ad in it.
If you want full control, you WILL have to pay for your own host. theres no way around it.
as for the types, there are many types. PHPBB is a common free type, but this board suffers from the "you get what you pay for" problems. It works well, but there many bugs and security exploits in it. But for free, it's good.
And it's pretty simple and straight forward. Just follow the install instructions and you're set.
may I suggest you to http://www.dreamhost.com/hosting.html
Put in this promo code for huge savings: 97MONKEY I have a account with them and it's very good service. They also have a very easy going TOA. Except for a few things(I think hate speech is not allowed, but could be wrong), you can put nearly anything up on your server that isn't illegal. And you get the most out of your buck from them, and it costs the average price of most other packages.
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How do i make forum?
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