ekj7: F1 shows an icon in the top-left corner. I'm not entirely sure what it is, maybe a crowbar and another melee weapon? F2 shows a gun, and F3 shows body armor. That's all though. Is it supposed to show a list of available items of that type underneath?
Yes, it shows a list of all items that you have collected and have not sold (not counting fists which you cannot sell - they are always on the list). You use the mouse wheel to move the current selection in that list, and click to make your choice. When you click/select, the game is unpaused and the menu disappears.
The weapon that you selected most recently, stays selected, even if you have holstered it (using 'h' key). Then you don't need to go back to the menu unless you want to change to a different weapon. If you click, you take a swing (or shot) at something (or nothing) with whatever weapon you selected last.
It sounds like you are seeing the menu but have not figured out how to use it? Or there is some malfunction preventing you from using it. I can't tell. At that stage in the tutorial you might have a crowbar plus your fists available. You should not yet have a gun (but I don't remember what that menu looks like before you acquire any guns). On F3 you should see your starter clothes because you haven't found anything else to wear yet.
At least, this is how it's supposed to work.