You have a max of 10 points for each S.P.E.C.I.A.L category. As you've seen, there's a perk-tree under each one. Some of these perks can only be opened when you've reached a specific number of points for that particular S.P.E.C.I.A.L category. Once enough points have been gained you're not restricted to just opening the next perk down within the perk-tree. You can open any number of the perks offered, picking which one you want - so long as you have enough points to open it. Yes, some of the perks are automatically available from the start.
At the start of you're character build it's wise to spread your allocated number of points across a range of SPECIAL abilities. As an example, I put most of my points into Perception, Intelligence, Agility, Luck. Spreading what was left amongst the remaining SPECIAL categories.
Tip. If you want/choose to, you can google how to gain as many points as you chose to unlock all your SPECIAL's.