Would it be OK to host a forum with DreamHost? How big could it become?
It’s definitely OK to host a forum of legal content. How big depends on the software you run. If it becomes so big, by then you should be making enough money off of it to upgrade to PS or beyond.
Another possibility for a big forum is to use the “easy” one-click install of phpbb. Since this is actually hosted on servers specifically customized for fast and scaleable phpbb hosting, I’d guess that they’d be superior to a shared hosting experience.
You would be limited to the plug-ins that are installed by default.
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And limited to the existing theme(s).