I've now hit level four but the only perks available to me are still stat increases. All the perks at L01 and below are greyed out, and unselectable, even if I meet the pre-requistes. Is this expected behaviour? Is there something else I need to do to get other perks?
The perks screen uses fading to indicate a skill you don't have, and outlining to indicate a skill you can't have (due to not meeting the requirements), see this screenshot here:
If you've got skills that are faded out, you should be able to get these by clicking on them and then pressing the confirmation key as prompted at the bottom of the screen:
If the perk is outlined entirely, hovering over the perk will still tell you what it does but also inform you of why it's outlined (not enough strength in my case).