My suggestion is to like or tweet most of your threads. And I don't mean your members' threads. I mean threads you made, from your own fingers. Why? Because your tweets has to reflect your website's brand and/or your brand. Your website's brand is your brand and then vice versa. You need to get people to trust your posts, your threads, your tweets, and your likes. Because if your twitter followers don't like a thread created by a member of your forum, then it reflects your entire site's brand, which in turn hurts your brand. This is true of any website. ANY.
The only time that I would tweet or like a members' thread is when the site has become strong. You don't need to worry about branding after a website has established it's presence. So, if your friend comes over your site and makes a thread about his youtube video, tweet that. And then put in your marketing speech. Make it relevant to that thread.