You can also cover both bases and have your forums based at, say, forums.mydomain.com and then use a 301 redirect at mydomain.com/forums

Does it mean that we should register a sub-domain with our host and then redirect it to directory via 301 redirect?
Yes that will be better... Just make the forum in a sub directory and then do the redirect to mydomain.com/forum from forum.mydomain.com
I see many forums using this method. It works. You'll have more chances to get higher rankings in SEs