You don't need a VPS. Shared hosting is fine, and probably recommended for a site just starting out.
If they are telling you that you need a VPS, you may want to look for another hosting provider as it sounds like they are trying to upsell you.
Another option is the cloud offering available from XenForo.
As for where to put it. In the root of the location of the shared hosting provider (usually /www or /html or similar).