I'm launching a forum for foreigners in Taiwan. Right now, I don't have much money so I purchased a shared web hosting server at Dreamhost (The Happy Hosting Plan, which is around 9 US dollars a month). Is it a bad idea? I can just migrate the site to a new dedicated server when I get more users, but I'm not sure if this waht most forum web masters do.
Starting out on budget shared hosting (provided it performs adequately and allows permissions for all the back-end functionality you require) is the sensible option. There is no point launching a brand new forum on a dedicated server.
You can get a shared hosting plan from anything from free to $10 that is perfectly suitable for your needs - the one your on sounds just fine.
Migrating a forum/community is simple enough though is obviously specific to the software you're using.
You might find that the next stage may be to a VPS or cloud environment rather than making the leap to a (probably quite expensive) managed dedicated solution.
I think it is a good idea, although I do not know what your initial visitors could is going to be. But I can tell you that the shared hosting do offer a lot of traffic.
It is also worth checking out websites like cloudflare they are a sort of CDN, they cache your static files and help to speed up your website.
And of course when your website get's bigger, you can upgrade your package. If you choose a good CMS the migration won't be any problem.