Hi Jenny,
My first observation in dealing with the email component is that you can't make the unsubscribe link dynamic based on segments via the Unsubscribe HTML in the Admin area.
One (longish) workaround: you
could remove the unsubscribe code from Admin and manually plug it into every single one of your emails via the actual email editor. This would allow you to drop the section into a dynamic segment. But it's also somewhat risky, as you never want to send out marketing emails without an unsubscribe footer, even by accident.
Now, the second choice you describe, making the form on the actual landing page dynamic based on segment membership, is perfectly feasible. Toggling this is slightly different than in the email editor, but fairly simple. Just select the form on your page so that the gear icon shows up in the right corner. Click on it and select "Segment by". Since you said you set up your segments already, simply select the segment that represents your client/prospect breakdown. From here you should be able to select the form that you want to appear for each segment. Close and approve as normal and you're all set.
Hope this helps.