If something says "any martial/simple weapon" in character creation I think it includes ranged weapons too, but does it include ammunition? Does my bow come with arrows?
Typically when it lists a bow or simple crossbow specifically in the equipment list, it is accompanied with the text "and 20 bolts" or "and 20 arrows."
I'd argue that choosing an ammunition weapon would come with same amount of ammunition, as RAI.
I could see a DM arguing the opposite, "Since it doesn't say you get ammo, you need to buy it." Because it is Rules As Written.
Since 20 bolts or 20 arrows cost 1 gp, and 20 sling bullets cost 4 cp, I don't see a reason why this should be a sticking point either way. It's not game breaking to start with it, and it isn't bank breaking to buy it. The only problem I see is if the DM lets you have the weapon, and you assume you have the ammo until you go to use it.
Ask your DM.
If a class or background starting package gives you any simple or martial weapon then that means a weapon on the weapon table.
By strict reading, arrows are not simple or martial weapons and you would have to buy them out of the cash you get. By a broader reading that the intent is to give you a weapon you can actually use, they would be included.