I don't think it counts the various puzzle items, but I don't really know.
Theres plenty of items out there though, so you really shouldn't worry about getting the 150 you need. Theres no need to go way off the path to get extra items (so for example, don't head way down towards the historical center when you're supposed to be going to the bowling alley), and just picking up all the items along the way is plenty.
Time shouldn't be an issue anyway though if you opt for the dog/ufo ending and you know where to go, so theres no need to be thinking about shaving off seconds by seeing how many items you can skip.
If you're super interested just for the sake of knowing, you could probably do a melee only run on easy without picking up any health/ammo (or at least, keeping track of what you do pick up) and see what your final item count is.
In my experience, SH3 counts quest items as another item. This is because during the last part when you're putting the tarot cards in the door, if you take one, it lags (due to the achievement trying to unlock).
This feels warm. What is this feeling? Is it of warmth?