You may end up liking Muut, but I find it a complete disaster. Almost impossible to follow threads or do meaningful searches. It's a super simple forum. If you only have occasional discussions then it may be fine. I know a couple of developers who use it for their products and ... well ... there's simply nothing nice to say about the experience. But if you like it then use it.
I'm not really sure what your needs are. With almost all forum software you can include a link in the header back to your website, and visa versa. That's probably the simplest way to go and then you can have a "proper" forum coordinated with your website. It also opens up a lot of options for you.