was thinking should certain player classes have access to either the monster manual or be able to write their own. like druids and rangers for example. to me it would make sense for a hunter to make notes on certain animals that he has encountered and keep track on how he beat them how many attacks they could handle. now personally i would go with after encounter do a gather information check and if successful allow them to copy the monster manual entry into their characters log book. otherwise if they just got to use monster manual they would be able to look at any creature they wanted
I don't see it as a major problem to let the players read the MM, after all a lot of them own a MM themselves and there is nothing you can do to prevent them from reading it at home!
But I would stay far away from making assumptions like the above, on the ground that "it makes sense", because often the opposite assumptions makes sense as well.
A hunter learns to know her prays sure, but it is a very strong assumption that a hunter in a fantasy world has the opportunities for fighting a lot of creatures of the same type, except for harmless game like deers and hares.
If you say that a Ranger with a chosen favored enemy (the best candidate for this) should be allowed access to full stats of monster X, you are implying that there are plenty of monster X in the world in the first place, that the Ranger has actually met several of monster X and survived, or there are reliable books available written by people who have, and that it has been possible to figure out the details (the characters don't know "numbers" but if the player has them available, we can say the character is aware of whatever equates to those numbers in fantasy world terms).
Are they reasonable assumption? Yes.
Should you take them for granted? Hell, NO!
When I DM a game, my typical fantasy world setup is "low-magic medieval europe-styled points of darkness". That actually means the world is
not full of monsters and most importantly is
not full of books.
OTOH there's nothing wrong with setting the game in a world where monsters are a common sights, and you can find manuals and teachers in every village.
So before you make those assumptions you must check with your DM and understand what kind of fantasy setting she is running.